If a random variable X with the following distribution has mean value of 0.6, find -1 ON 0.2 2 0,1 3 0.2 POXx) 11 n a) the value of m and the value of n b) P(X<=1) c) variance of X d) expected value of Y=3X+1 e) variance of Y=3X+1
Answers
The given distribution has mean value of 0.6. The values of m and n can have multiple solutions. sum of the probabilities P(X<=1) is 0.5, variance of X is 2.11, expected value of Y=3X+1 is 4.9, and variance of Y is 19.0.
The given distribution can be represented as follows:
X -1 0.2 2 0.1 3
P(X) 0.2 0.2 0 0.1 0.5
To find the mean value of X, we use the formula:
E(X) = Σ [ xi * P(X = xi)
E(X) = (-1 * 0.2) + (0.2 * 0.2) + (2 * 0) + (0.1 * 0.1) + (3 * 0.5)
E(X) = 1.3
Since E(X) = 0.6, we can set up the following equation:
E(X) = Σ [ xi * P(X = xi) ] = 0.6
(-1 * 0.2) + (0.2 * 0.2) + (2 * 0) + (0.1 * 0.1) + (3 * 0.5) = 0.6
Simplifying this equation gives us:
0.1 + 1.5 = m * n
m * n = 1.6
We can choose any values of m and n that satisfy this equation. For example, we can choose m = 1 and n = 1.6, or m = 2 and n = 0.8.
P(X <= 1) is the sum of the probabilities of all values of X less than or equal to 1:
P(X <= 1) = P(X = -1) + P(X = 0.2) + P(X = 0.1)
P(X <= 1) = 0.2 + 0.2 + 0.1
P(X <= 1) = 0.5
The variance of X can be found using the formula:
Var(X) = E(X^2) - [E(X)]^2
To find E(X^2), we use the formula:
E(X^2) = Σ [ xi^2 * P(X = xi) ]
E(X^2) = (-1)^2 * 0.2 + 0.2^2 * 0.2 + 2^2 * 0 + 0.1^2 * 0.1 + 3^2 * 0.5
E(X^2) = 4.3
Then, we can calculate the variance:
Var(X) = E(X^2) - [E(X)]^2
Var(X) = 4.3 - 1.3^2
Var(X) = 2.11
The expected value of Y = 3X + 1 can be found using the formula:
E(Y) = E(3X + 1) = 3E(X) + 1
E(Y) = 3(1.3) + 1
E(Y) = 4.9
To find the variance of Y, we use the formula:
Var(Y) = Var(3X + 1) = 9Var(X)
Var(Y) = 9(2.11)
Var(Y) = 19.0
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Related Questions
Please show work
Thank you:)
Answers
<CAB= 56°
(DC= 78°
(DB= 78+56=134°
<DAB=134°
(BED=360-134= 226°
(BEC=226+78=304°
(CED= 360-78=282°
hey:) I hope this was correct and helpful
Kent Co. manufactures a product that sells for $60.00. Fixed costs are $285,000 and variable costs are $35.00 per unit. Kent can buy a new production machine that will increase fixed costs by $15,900 per year, but will decrease variable costs by $4.50 per unit. What effect would the purchase of the new machine have on Kent's break-even point in units?
Answers
0riginal break even point:
285000/ 60/35 = $166,250
New break even point = new fixed costs / ( selling price - variable cost/ selling price)
New break even point = 285,000 + 15,900. / ( 60-( 35-4.50)/60
300,900 / 60-30.50/60 = $612,000
The new break even point increases.
Which translation will change figure ABCD to figure A'B'C'D'?
A. 8 units left and 6 units up
B. 6 units left and 7 units up
C. 7 units left and 5 units up
D. 5 units left and 6 units up
Answers
Answer:
Option A 8 units left and 6 units up
What is $+%
WRONG ANSWERS ONLY
MAKE THE ANSWER A LONG ANSWER
EXPLAIN HOW YOU GOT YOUR ANSWER
MAKE IT KINDA MAKE SENSE
I WILL GIVE BRAINLIEST
Answers
Answer:
$%
Step-by-step explanation:
cause x to the square root of 27 x 9382 is equal to the penguin race that gives us $%
Glad i could help!
please help need asap
Answers
Answer: X = 21/6
Step-by-step explanation:
The angle is a 90 degree angle.
that means we know 21x+6=90
21x = 90-6
21x=84
x = 84/24
x = 21/6
x = 21/6
uestion Progress
Homework Progress
7/48
Simplify
2x + x + x + 2y x 3y x y
Answers
Answer:
4x+6y^3
Step-by-step explanation:
2x+x+x+2y*3y*y
4x+6y^3
The speed of light is 3 x 108 m/s. If its frequency is 4.11 x 104 Hz, what's is its wavelength.
PLZZ HELP PLZZ ill give thanks n more :(
Answers
Wave length = speed / frequency
Wave length = 3x10^8 / 4.11x10^4
Wave length = 7.299x10^3nm
A number is multiplied by 8, and that product is added to 2. The sum is equal to the product of 2 and 25. Find the number.
Answers
Answer: the number = 6
Step-by-step explanation:
Let x be the number.
Set equation according to the information given
2 + 8x = 2 × 25
Simplify by multiplication
2 + 8x = 50
Subtract 2 on both sides
2 + 8x - 2 = 50 - 2
8x = 48
Divide 8 on both sides
8x / 8 = 48 / 8
\(\boxed {x=6}\)
Hope this helps!! :)
Please let me know if you have any questions
Carol uses this graduated tax schedule to determine how much income tax she owes. A 3-column table with 6 rows. Column 1 is labeled If taxable income is over with entries 0 dollars, 7,825 dollars, 31,850 dollars, 64,250 dollars, 97,925 dollars, 174,850 dollars. Column 2 is labeled but not over with entries 7,825 dollars, 31,850 dollars, 64,250 dollars, 97,925 dollars, 174,850 dollars, no limit. Column 3 is labeled the tax is with entries 10 percent of the amount over 0 dollars, 782 dollars and 50 cents plus 15 percent of the amount over 7,825 dollars, 4,386 dollars and 25 cents plus 25 percent of the amount over 31,850 dollars, 12,486 dollars and 25 cents plus 28 percent of the amount over 64,250 dollars, 21,915 dollars and 25 cents plus 33 percent of the amount over 97,925 dollars, 47,300 dollars and 50 cents plus 35 percent of the amount over 174,850 dollars. If Carol’s taxable income is $89,786, how much income tax does she owe, to the nearest dollar? a. $25,140 b. $12,654 c. $19,636 d. $37,626
Answers
Answer:
answer is c) $19,636
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
1) True or False: Solving a system of equations using the graphing, substitution, or elimination method will find the exact same solution.
2) True or False: Elimination can never be used to solve a nonlinear system of equations (a system where one equation is not linear).
Answers
True: Solving a system of equations using the graphing, substitution, or elimination method will find the exact same solution.
False: Elimination can never be used to solve a nonlinear system of equations (a system where one equation is not linear).
What is a system of equations?A system of equations can be defined an algebraic equation that only has two (2) variables and can be solved simultaneously.
In Mathematics, there are three (3) main methods that are commonly used for solving a system of equations simultaneously and these include the following:
Graphing method.Substitution method.Elimination method.Generally speaking, the same solution would be obtained when any of the three (3) methods for solving a system of equations are used. However, it is completely false to state that the elimination method cannot be used to solve a nonlinear system of equations.
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A school photographer just bought a new memory card for her camera. She took 2 pictures
to check that everything is working properly. Now that it's picture day, she expects to take 5
pictures of each student.
Write an equation that shows the relationship between the number of students photographed,
x, and the total number of pictures on the memory card, y.
00
Answers
Answer:
5x+2
Step-by-step explanation:
the pattern is
y is 5 times x plus 2
y=5x+2
The solution is, y=5x+2, an equation that shows the relationship between the number of students photographed, x, and the total number of pictures on the memory card, y.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
She took 2 pictures to check that everything is working properly.
Now that it's picture day, she expects to take 5 pictures of each student.
now, we get,
the pattern is
y is 5 times x plus 2
y=5x+2
Hence, The solution is, y=5x+2, an equation that shows the relationship between the number of students photographed, x, and the total number of pictures on the memory card, y.
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A total of 50 randomized samples were assigned into 5 different treatment groups in a pharmaceutical science experiment. Each group includes 10 persons (subjects). In order to test if any difference is discernible among these 5 treatments, one-way ANOVA was conducted for the study. Here are data we calculated: Sum of square between group = 232. Sum of square within group = 400.Subject Treatment 1 Treatment 2 Treatment 3 Treatment 4 Treatment 51 2
---
10ANOVA Summary Table
Source Sum of Square Degree of freedom Mean Square F
Between 232
Within 400
Totala. State null hypothesis and alternative hypothesis. b. Calculate the degree of freedom between group, and the degree of freedom within group. c. Mean squares between groups. d. Mean squares within groups.e. F ratiof. If critical value of F is 2.61, should we reject or accept the null hypothesis?g. State your conclusion for this research.
Answers
The null hypothesis is that there is no discernible difference among the 5 treatments. The alternative hypothesis is that there is a discernible difference among the 5 treatments
How to calculate the valuesDegree of freedom between groups is nothing but the number of treatments-1 i.e. 5-1=4 and degree of freedom within groups is nothing but total number of subjects- number of treatments i.e. 5*10-5=50-5=45
Mean squares between groups is calculated as follows:
Mean squares between groups= Sum of squares between groups/degrees of freedom between groups= 232/4=58
Mean squares within groups is calculated as follows:
Mean squares within groups= Sum of squares within groups/degrees of freedom within groups= 400/45= 8.89 rounded off to two decimal places
F ratio is calculated as follows:
F= Mean squares between groups/Mean squares within groups
= 58/8.89
= 6.524184477
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graph the line passing through (−4,−1) whose slope is m=-4/5
Answers
Answer:
\(y=-\frac{4}{5}x-\frac{21}{5}\)
Step-by-step explanation:
The fastest way is to use point-slope form with \(m=-\frac{4}{5}\) and \((x_1,y_1)=(-4,-1)\):
\(y-y_1=m(x-x_1)\\y-(-1)=-\frac{4}{5}(x-(-4))\\y+1=-\frac{4}{5}(x+4)\\y+1=-\frac{4}{5}x-\frac{16}{5}\\y=-\frac{4}{5}x-\frac{21}{5}\)
To graph the line passing through (-4,-1) with slope m = -4/5, we can use the slope-intercept form of the equation of a line, which is:
y = mx + b
where m is the slope and b is the y-intercept.
Substituting m = -4/5, x = -4, and y = -1, we can solve for b:
-1 = (-4/5)(-4) + b
-1 = 3.2 + b
b = -4.2
Therefore, the equation of the line is:
y = (-4/5)x - 4.2
To graph the line, we can plot the given point (-4,-1) and then use the slope to find additional points. Since the slope is negative, the line will slope downwards from left to right. We can find the y-intercept by setting x = 0 in the equation:
y = (-4/5)x - 4.2
y = (-4/5)(0) - 4.2
y = -4.2
So the y-intercept is (0,-4.2).
Using this point and the given point (-4,-1), we can draw a straight line passing through both points.
Here is a rough sketch of the graph:
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The point (-4,-1) is marked with an asterisk (*), and the y-intercept (0,-4.2) is marked with a dash. The line passing through these two points is the graph of the equation y = (-4/5)x - 4.2.
can someone heelp me plz
Answers
Answer:
1052 is MLII, 450 is CDL, 952 is CMLII, and 942 is CMXLII.
Step-by-step explanation:
For 1052, M=1000 L=50 and II= 2 and if you add all those you get 1052. For 450, CD=400 and L=50 and if you add all those up then you get 450. For 952, CM=900 L=50 and II=2 and if you add all those up then you get 952. For 942, CM=900 XL=40 and II=2, and if you add all those up then you get 942.
A clothing company makes a profit of $2.3 million. This is $4.1 million more than last year. What was the profit last year?
Answers
Answer:
-1.8 million. This means that the business likely spent a lot on production and generated very little sales during the first year.
Step-by-step explanation:
2.3 - 4.1= -1.8
Please help ASAP!!! Thank you so much!!! Just want confirm my answer and it is A) -5. Consider the function f(x)= \(x^{3}\) +4\(x^{2}\)-25x-50. (x^3+4x^2-25x-50). If there is a remainder of 50 when the function is divided by (x-a) what is the value of a? A) -5 B) -2 C)-3 D)
Answers
Answer:
Correct is A
Step-by-step explanation:
Correct is A , notice that when you perform synthetic division you get that the reminder is 50, please refer to the image I attach to see it.
What are the ordered pairs of the
solutions for this system of equations?
f(x) = x2 – 2x + 3; f(x) = –6x
(-3, [?]); ([ ]), ([ ])
Answers
Answer:
\( {x}^{2} - 2x + 3 = - 6x \\ = {x}^{2} - 2x + 6x + 3 = 0 \\ \\ = {x}^{2} + 4x + 3 = 0 \\ = (x + 1)(x + 3) \\ = x = - 1and \: x = - 3\)
Which expression is NOT equivalent to the expression 8m + 12?
A - 1/2 (16m + 24)
B - 4 (2m + 3)
C - 2 (4m + 6)
D - 8 (m +12)
Answers
Answer:
D
Step-by-step explanation:
6. Which of the following strategies can
help you solve 4 x 6? Select all that
apply.
(6x6) + (6 x 6)
(4 x 3) + (4 x 3)
(5x5)+(4x 1)
(5x4) + (1x4)
(2x4) + (2x6)
Answers
Answer:
(4x3) + (4x3) and (5x4) + (1x4)
Step-by-step explanation:
When you multiply 4 by 3 you get 12. And 12 + 12 is 24. 4 x 6 is 24 so then that is an answer. And 5 by 4 is 20 and 1 x 4 is 4 you add them you get 24.
Determine f(-a) where f(x) = x2 - 6x and simplify.
Answers
Answer:
6a
Step-by-step explanation:
replace x with -a
-2a -6(-a)
-2a +8a
6a
7. Resolver: Cuantas cajas de 30cm*90cm* 78 cm
caben en un contenedor de 180cm*4m*2m
Answers
Answer:
Ninguna
Step-by-step explanation:
Porque las dimensiones de las cajas son mucho más grandes que las del contenedor.
(tal vez la pregunta este mal formulada)
A fair die with its faces numbered from 1 to 6 will be rolled. Which of the following is the best interpretation of the probability that the number landing face up will be less than 3?
For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 1/3
For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 1/2
For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 2/3
For three rolls of the die, a number less than 3 will land face up one time.
It will take three rolls of the die before a number less than 3 lands face up for the first time.
Answers
The best interpretation of the probability that the number landing face up will be less than 3 is \(\frac{1}{3}\).
For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is \(\frac{1}{3}\).
As per the given question a fair die with its faces numbered from 1 to 6 will be rolled.
Here we have to calculate the probability that the number landing face up will be less than 3.
The event of the number landing face up will be less than 3 is exhaustive, mutually exclusive, and independent face of a die = 6
(1, 2, 3, 4, 5, 6)
Favorable number of faces of a die = 2
(1, 2)
Since the number landing faces up will be less than 3.
Therefore the probability that the number landing face up will be less than 3
\(=\frac{\text { Favourable Number }}{\text { Total Number }}$\)
\(& =\frac{2}{6} \\\)
\(& =\frac{1}{3}\)
Therefore the best interpretation of the probability that the number landing face up will be less than 3 is \(\frac{1}{3}\)
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The long-run relative frequency of a number less than 3 landing face up is 2/3.
The best interpretation of the probability that the number landing face up will be less than 3 is that for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 2/3. This can be expressed mathematically as P(x<3) = 2/3, where P(x) is the probability of the number landing face up being less than 3.
For a single roll of the die, the probability of a number less than 3 landing face up is 1/2. This is because there are three numbers (1,2,3) which are less than 3, and 6 possible outcomes. Therefore, the probability of any one of those three numbers landing face up is 3/6, or 1/2.
For multiple rolls of the die, the probability of a number less than 3 landing face up is the sum of the probabilities of each of those three numbers landing face up. This can be expressed mathematically as P(x<3) = (1/2) + (1/2) + (1/2), or 2/3.
Therefore, for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 2/3.
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On a piece of paper, use a protractor to construct a triangle with angle measures of 40° and 60º.
What is the measure of the third angle?
Answers
Answer:
80
Step-by-step explanation:
every triangle, no matter what shape or size, will have all angles add up to 180 degrees so 180-40-60=80
What are the coordinates of vertex C'after rotating the figure 180° about theorigin?у6BID42A АEXo024 6A. (-6,4)B. (4.-6)C. (4,6)D. (-4,-6)
Answers
Vertex C (4, 6 ) Rotation 180º about the origin CCW c' (-4, -6)
C (x, y ) C ' (-x, -y )
________________
Answer
Option D
Ishi walked a total of 2 1/2 miles on a treadmill. He walked a constant sate of 4 MI per hours. Which expressions shows how long, in minutes, Ishi walked on the treadmill?
Answers
Answer:
Time taken T = 2.5 miles/ 0.067 miles per minute
Step-by-step explanation:
In this question. We are asked to give the expression that shows how long in minutes that should be walked on the treadmill.
Now, let’s look at what we have in the question. We have a distance of 2.5 miles and a speed of 4 mph, read as 4 miles per hour.
The question is a term of how long. This means what we are trying to calculate refers to the time taken to walk a total of 2.5 miles on the treadmill at a speed of 4mph.
Mathematically, we know that the time taken would be equal to the distance walked on the treadmill mill divided by the speed used to walk this distance over the treadmill.
This can be written in the equation form as T = D/S
Now if we look at our speed, it is written in hours, but the question stipulated minutes. So what do we do? We simply make a conversion from 4mph to 4mpm. To do this , we simply divide 4mph by 60 to give 0.067mpm.
We now move on to write the time taken. This would be:
T = 2.5 miles/0.067 miles per minute
Answer:
Its 2.5 miles divided by 4 miles/hour times 60 minutes/1 hour
Step-by-step explanation:
find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (hint: let (x,y) be the unknown endpoint. apply the midpoint formula, and solve the two equations for x and y.) midpoint (-15, -6), end point (-16,-3)
Answers
The coordinates of the other endpoint of the segment, given its midpoint and one endpoint are (-14, -9)
How to find the midpoint coordinate of a Line?The Midpoint Formula for a line with endpoints as (x₁, y₁) and (x₂, y₂) is;
((x₁ + x₂)/2, (y₁ + y₂)/2)
We are given the following;
Midpoint (-15,-6)
End point (-16,-3)
Let x₁ = -16, the x coordinate of the endpoint
Let x₂ = the x coordinate of the unknown endpoint
Let y₁ = -3, the y coordinate of the endpoint
Let y₂ = the y coordinate of the unknown endpoint
Thus, for the x coordinate of the unknown endpoint;
(x1 + x2)/2
(-16 + x₂)/2 = -15
-16 + x₂ = -30
x₂ = -14
For the y coordinate of the unknown endpoint;
(y1 + y2)/2
(-3 + y₂)/2 = -6
-3 + y₂ = -12
y₂ = -12 + 3
y₂ = -9
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it costs $50 to join a gym plus $28 per month define the variable
Answers
Answer:
28
Step-by-step explanation:
because it's value increases by 28 every month
After 4 years you have 5300 what is the initial deposit if the account pays 2.5% annual interest compounded continuously
Answers
Answer:
Initial deposit P = 4,801 (Approx.)
Step-by-step explanation:
Given:
Amount after 4 year = 5,300
Number of year = 4 year
Rate = 2.5% = 0.025
Find:
Initial deposit
Computation:
A = P[1+r]ⁿ
5,300 = P[1+0.025]⁴
5,300 = P[1.025]⁴
5,300 = P[1.1038]
Initial deposit P = 4,801 (Approx.)
A coin is flipped eight times where each flip comes up either heads or tails. How many possible outcomes a) are there in total
Answers
Answer:
256 outcomes.
Step-by-step explanation:
Each time you flip the coin you have two possible outcomes, it can either come up with heads or tails.
You're going to flip the coin eight times so the first time you can have 2 possible outcomes, the second time you have 2 possible outcomes, the third time you have 2 possible outcomes, etc.
Since you are going to do this eight times you are going to multiply each of the outcomes, so you will have:
Possible outcomes = 2×2×2×2×2×2×2×2= 256
Thus, there are 256 different outcomes in total.
Help me please!!!
Whoever answers right gets brainliest!
Answers
The equation that best describes the relation is y = -x+1 ( optionD)
What is linear equation?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Taking x(0,1) and y ( 1,0)
therefore the slope of the line
= 0-1/1-0
= -1/1 = -1
the equation a line is given as
y-y1 = m(x-x1)
= y-1 = -1( x - 0)
= y-1 = -x
y = -x +1
therefore the equation that describe relation is y = 1-x or y = -x+1
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