16. Suppose that E(X) = μ and Var (X) = σ2. Let Z = (X − μ)/σ. Show that E(Z) = 0 and Var(Z ) = 1.
Answers
It is shown that the expected value of Z is of 0, while it's variance is of 1.
How to obtain the expected value and variance?The z-score formula is defined as follows:
Z = (X − μ)/σ.
In which the parameters are given as follows:
X is a score in the distribution.μ is the mean of the distribution.σ is the standard deviation of the distribution.The expected value of X is equals to the mean, hence the expected value of Z is calculated as follows:
E(Z) = (E(X) − μ)/σ
E(X) = μ, hence the numerator is of zero, with the division of zero by the constant standard deviation resulting in zero, hence it is shown that E(Z) = 0.
For the variance, we have that:
Var(Z) = (Var(X) − μ)/σ
We have that:
Var(X) = σ², Var(μ) = 0, Var(σ) = σ² (as the variance is the standard deviation squared).
Hence the variance of Z is given as follows:
Var(Z) = σ²/σ²
Var(Z) = 1.
More can be learned about the z-score formula at https://brainly.com/question/25800303
#SPJ1
Related Questions
help please help mesda
Answers
Answer:
25, 25, 22.5, 22
Step-by-step explanation:
It gives you a hint; K = y/x. They give you what x and y are so use that to solve for the last row.
We are given all of these values:
x -> 2, 3, 4, 5
y -> 50, 75, 90, 110
Use the formula given and solve for K.
50/2 = 25
75/3 = 25
90/4 = 22.5
110/5 = 22
Best of Luck!
A precise statement of the qualities of an idea, object, or process is called a
O A. theorem
O B. proof
C. definition
D. common notion
Answers
Answer:
C. definition
Step-by-step explanation:
A precise statement of the qualities of an idea, object, or process is called a definition. Hence, option (C) is answer.
5/8 entre 6 personas
Answers
Based on the information we can infer that 5/8 between 6 people is equal to 15/24.
How to divide 5/8 between 6 people?To calculate the part that corresponds to each person, divide the fraction 5/8 by the number of people, which in this case is 6. To simplify the fraction, you can reduce the numerator and denominator by dividing both by their maximum common factor, which is 3.
5 ÷ 3 = 1 and 2 remainder8 ÷ 3 = 2 and 2 remainder
So the fraction can be simplified to 1 2/8, which can also be expressed as 1 1/4 or 5/4 in its most simplified form. This means that each person would receive 5/4 of the original share, and since there are 6 people in total, you can multiply 5/4 by 6 to get the total share that corresponds to all 6 people:
(5/4) x 6 = 30/4 = 15/2 = 15/24
So each person would receive 15/24 of the original amount.
Note: Here is the question in English:
5/8 divided in 6 people
Learn more about fractions in: https://brainly.com/question/28021779
#SPJ1
which of the following is not a characteristic of both surveys and observational studies?
a. the researcher direct control over at least one variable
b. data are collected about population
c. the researcher does not control or change the population
d. results are not used to prove cause and effect
Answers
The characteristic of the researcher having direct control over at least one variable to both surveys and Observational .
The option that is not a characteristic of both surveys and observational studies is:
a. The researcher has direct control over at least one variable.
Surveys and observational studies have several characteristics in common, such as collecting data about a population and not proving cause and effect. However, the characteristic of the researcher having direct control over at least one variable is not applicable to both surveys and observational studies.
In a survey, the researcher collects data by asking questions to individuals or groups. They do not have direct control over the variables being studied but rather collect information based on participants' responses. The researcher's role is primarily in designing the survey, selecting the sample, and analyzing the data.
In an observational study, the researcher observes and records data without intervening or manipulating any variables. The researcher does not have control over the variables being observed; instead, they observe and document the existing conditions or behaviors.
the characteristic of the researcher having direct control over at least one variable is not applicable to both surveys and observational studies. Both methods involve data collection about a population and do not establish cause and effect relationships, but control over variables is not a shared characteristic.
To know more about Observational .
https://brainly.com/question/14354714
#SPJ11
Solve using tangent and cosine
Answers
The value of side length x in diagram a) is 4.3mm and side length x in diagram b) is 309.7 m.
What are the sides of the triangle labelled x?The figures in the image are right triangles.
A)
angle D = 17 degree
Adjacent to angle D = 14 mm
Opposite to angle D = x
To solve for the missing side length x, we use the trigonometric ratio.
Note that: tangent = opposite / adjacent
Hence:
tan( 17 ) = x/14
x = tan( 17 ) × 14
x = 4.3mm
B)
angle Z = 82 degree
Adjacent to angle Z = 43.1 m
Hypotenuse = x
Using trigonometric ratio,
cosine = adjacent / hypotenuse
cos( 82 ) = 43.1 / x
x = 43.1 / cos( 82 )
x = 309.7 m
Therefore, the measure of x is 309.7 meters.
Learn more about trigonometric ratio here: brainly.com/question/28016662
#SPJ1
What is the area of the triangle?
Answers
Answer:
your answer is B (14)
Step-by-step explanation:
add 6+8=14
brainliest?
Answer:
24 cm
Step-by-step explanation:
area of a triangle is 1/2 BH
Question: 18 of 19
Lesson 18
Find the component form of the following vectors. Round your answers to the tenth.
Magnitude of v = 50, direction angle 0 = 50°
Choice 'A' OV
Choice 'B'O V
Choice 'C'OV
Choice 'D' OV
(38.3, 32.1)
(33.8, 31.2)
(32.1, 38.3)
(31.2, 33.8)
4
Answers
The component form of the following vectors is Option A. V = (38.3, 32.1).
To find the component form of a vector given its magnitude and direction angle, we can use trigonometry.
The component form of a vector in two dimensions is represented as (x, y), where x is the horizontal component and y is the vertical component.
In this case, the magnitude of the vector is given as 50, and the direction angle θ is 50°. We can use this information to calculate the horizontal and vertical components.
The horizontal component (x) can be found using the formula x = magnitude * cos(θ), and the vertical component (y) can be found using y = magnitude * sin(θ).
Let's calculate the components:
x = 50 * cos(50°) ≈ 38.3
y = 50 * sin(50°) ≈ 32.1
Rounding the answers to the nearest tenth, we get the component form of the vector V as (38.3, 32.1).
Therefore, the correct answer is A. V = (38.3, 32.1).
Know more about the vectors here:
https://brainly.com/question/30854499
#SPJ8
The question is incomplete. Find the full content below:
Find the component form of the following vectors. Round your answers to the tenth.
Magnitude of v = 50, direction angle θ = 50°
A. V = (38.3, 32.1)
B. V = (33.8, 31.2)
C. V = (32.1, 38.3)
D. V = (31.2, 33.8)
show your solution and answer the 4 questions.
Answers
Answer:
Step-by-step explanation:
1. When the number of kilograms of paper is doubled, the points will be doubled
2. 300÷ 5 = 60
They have to collect 60 Kg of papers to earn 300 points.
3) P = 5*n
P = 5n
4) We are not only reducing the waste, the collected paper can be reused or can be sent to recycling centers.
Write a ratio in simplest form to express 8 inches over 3 feet
Answers
Answer:
Step-by-step explanation:
8 inches : 3 feet
12 x 3 = 36 inches
8 inches: 36 inches = 2 inches: 9 inches
The ratio in simplest form to express 8 inches over 3 feet is 2:9.
To express the ratio of 8 inches to 3 feet in simplest form, we need to convert the measurements to a common unit.
Since both measurements involve length, we can convert inches to feet or feet to inches.
We know that 1 foot = 12 inches
So 3 feet = 12×3
=36 inches.
Now the ratio 8 inches over 3 feet is equal to 8 inches over 36 inches.
8/36
Divide numerator and denominator by 4:
2/9
Hence, the ratio in simplest form to express 8 inches over 3 feet is 2:9.
To learn more on Ratios click here:
https://brainly.com/question/1504221
#SPJ4
In the exponential decay function ƒ(x) = a • bx, the b is between 0 and 1.
True
False
Answers
False, In the exponential decay function ƒ(x) = a • bx, the b is between 0 and 1.
What is exponential decay function?
In mathematics, the term "exponential decay" refers to the process of a constant percentage rate decline in a value over time.
It can be written as y=a(1-b)x, where y represents the final amount, a represents the initial amount, b represents the decay factor, and x is the amount of time that has passed.
How do you calculate an exponential function?
The equation f(x) = ax, in which the input variable x appears as an exponent, describes an exponential function. Both the exponential function and the value of x are dependent on the exponential curve.
The exponential function, which has the form, is a significant mathematical function. f(x) = ax.
Learn more about exponential decay function
brainly.com/question/14355665
#SPJ1
Convert 4feet to inches
Answers
48 inches :)
Answer:
48
Step-by-step explanation:
multiply the length value by 12
the length is 4ft so you multiply it by 12
so
4×12=48
so the answer is 48
When Aidan had his picture taken, the photographer charged a $10 sitting fee and $6
for each sheet of pictures purchased.
a. Write a function for the situation.
b. State what x and y represent in the function.
c. Graph the function.
ASAP
Answers
Answer:
10y x 6x = y = sitting fee x = $6
Step-by-step explanation:
The function is y = 10 + 6x, where y represents the total charge and x represents the number of sheets.
What is a linear equation?It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.
If in the linear equation one variable is present then the equation is known as the linear equation in one variable.
Let's suppose the total charge is y and the number of the sheets is x.
So according to the problem:
y = 10 + 6x
Here y represents the total charge and x represents the number of sheets.
Thus, the function is y = 10 + 6x, where y represents the total charge and x represents the number of sheets.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ2
Ramesh and Suresh are 20 years and 12 years old, respectively. Find how many years ago, the age of Ramesh was twice that of Suresh.
Answers
Answer:
4 years ago
Step-by-step explanation:
y= Ramesh
x= Suresh
y-8=x
y=2x
Plug into each other:
x+8=2x
x=8
y=16
Suresh was 8 years old 4 years ago
Ramesh was 16 years old 4 years ago
Let Y1 and Y2 denote the proportion of time during which employees I and II actually performed their assigned tasks during a workday, The joint density of Y1 and Y2 is given by
f(y1,y2) = { y1+y2, 0<=y1<=1, 0<=y2<=1, 0, elsewhere
Required:
a. Find the marginal density function of Y1 and Y2
b. Find P(Y1 >= 1/2 | Y2 >= 1/2).
c. If employee II spends exactly 50% of the dayworking on assigned duties, find the probability that employee I spends more than 75% of the day working on similarduties.
Answers
Answer:
Step-by-step explanation:
From the information given:
The joint density of \(y_1\) and \(y_2\) is given by:
\(f_{(y_1,y_2)} \left \{ {{y_1+y_2, \ \ 0\ \le \ y_1 \ \le 1 , \ \ 0 \ \ \le y_2 \ \ \le 1} \atop {0, \ \ \ elsewhere \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \right.\)
a)To find the marginal density of \(y_1\).
\(f_{y_1} (y_1) = \int \limits ^{\infty}_{-\infty} f_{y_1,y_2} (y_1 >y_2) \ dy_2\)
\(=\int \limits ^{1}_{0}(y_1+y_2)\ dy_2\)
\(=\int \limits ^{1}_{0} \ \ y_1dy_2+ \int \limits ^{1}_{0} \ y_2 dy_2\)
\(= y_1 \ \int \limits ^{1}_{0} dy_2+ \int \limits ^{1}_{0} \ y_2 dy_2\)
\(= y_1[y_2]^1_0 + \bigg [ \dfrac{y_2^2}{2}\bigg]^1_0\)
\(= y_1 [1] + [\dfrac{1}{2}]\)
\(= y_1 + \dfrac{1}{2}\)
i.e.
\(f_{(y_1}(y_1)}= \left \{ {{y_1+\dfrac{1}{2}, \ \ 0\ \ \le \ y_1 \ \le , \ 1} \atop {0, \ \ \ elsewhere \ \\ \ \ \ \ \ \ \ \ } \right.\)
The marginal density of \(y_2\) is:
\(f_{y_1} (y_2) = \int \limits ^{\infty}_{-\infty} fy_1y_1(y_1-y_2) dy_1\)
\(= \int \limits ^1_0 \ y_1 dy_1 + y_2 \int \limits ^1_0 dy_1\)
\(=\bigg[ \dfrac{y_1^2}{2} \bigg]^1_0 + y_2 [y_1]^1_0\)
\(= [ \dfrac{1}{2}] + y_2 [1]\)
\(= y_2 + \dfrac{1}{2}\)
i.e.
\(f_{(y_1}(y_2)}= \left \{ {{y_2+\dfrac{1}{2}, \ \ 0\ \ \le \ y_1 \ \le , \ 1} \atop {0, \ \ \ elsewhere \ \\ \ \ \ \ \ \ \ \ } \right.\)
b)
\(P\bigg[y_1 \ge \dfrac{1}{2}\bigg |y_2 \ge \dfrac{1}{2} \bigg] = \dfrac{P\bigg [y_1 \ge \dfrac{1}{2} . y_2 \ge\dfrac{1}{2} \bigg]}{P\bigg[ y_2 \ge \dfrac{1}{2}\bigg]}\)
\(= \dfrac{\int \limits ^1_{\frac{1}{2}} \int \limits ^1_{\frac{1}{2}} f_{y_1,y_1(y_1-y_2) dy_1dy_2}}{\int \limits ^1_{\frac{1}{2}} fy_1 (y_2) \ dy_2}\)
\(= \dfrac{\int \limits ^1_{\frac{1}{2}} \int \limits ^1_{\frac{1}{2}} (y_1+y_2) \ dy_1 dy_2}{\int \limits ^1_{\frac{1}{2}} (y_2 + \dfrac{1}{2}) \ dy_2}\)
\(= \dfrac{\dfrac{3}{8}}{\dfrac{5}{8}}\)
\(= \dfrac{3}{8}}\times {\dfrac{8}{5}}\)
\(= \dfrac{3}{5}}\)
= 0.6
(c) The required probability is:
\(P(y_2 \ge 0.75 \ y_1 = 0.50) = \dfrac{P(y_2 \ge 0.75 . y_1 =0.50)}{P(y_1 = 0.50)}\)
\(= \dfrac{\int \limits ^1_{0.75} (y_2 +0.50) \ dy_2}{(0.50 + \dfrac{1}{2})}\)
\(= \dfrac{0.34375}{1}\)
= 0.34375
Twelve percent of your customers buy 4 desserts. How many desserts can you expect to sell to 500 people?
Answers
16,650 desserts will be sold to 500 people
How to calculate the number of desserts that will be sold to 500 people?12% of the customers bought 4 desserts
4 ÷ 12/100
4/0.12
= 33.3
1 customer will buy 33.3 desserts
The number of desserts that 500 people can buy can be calculated as follows
= 33.3 × 500
= 16,650
Hence 500 people will buy 16,650 desserts
Read more on desserts here
https://brainly.com/question/14231647
#SPJ1
What is the value of x?
07
0 7√2
O
O 14
O 14√/2
45°
7√2
Answers
The value of the side length x is equal to 14 using the trigonometric ratio of sine.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
sin45 = 7√2/x {opposite/hypotenuse}
√2/2 = 7√2/x {sin45 = √2/2}
x = 7√2 × 2/√2 {cross multiplication}
x = 7 × 2
x = 14
Therefore, the value of the side length x is equal to 14 using the trigonometric ratio of sine.
Read more about trigonometric ratios here: https://brainly.com/question/3457795
#SPJ1
Hurry please i need it ASAP
Answers
Hmm, thats wrong actually, I believe its C?
Someone someone help me answering this question please
Answers
Answer:
Step-by-step explanation:
=mean=sum of data /no of data
=2+3+4/3
=9/3
=3
filling in for the dude that ran out of hundreds
Answers
Answer:
lollllll
Step-by-step explanation:
thanks for the points
helppp it's urgent and I don't understand dhow to do this please.
Answers
Answer:
i) Consecutive interior angles
ii) Supplementary angles
iii) The two oars are parallel by consecutive interior angles theorem
Step-by-step explanation:
i) m∠1 and m∠2 lie between two line and on the same side of the line passing through the two lines. Therefore, they are consecutive interior angles
ii)x = 10
m∠1 = 6x + 18
= 6(10) + 18
= 60 + 18
= 78
m∠2 = 9x + 12
= 9(10) + 12
= 90 + 12
= 102
m∠1 + m∠2 = 72 + 108 = 180
Since m∠1 and m∠2 add to 180, they are supplementary angles.
iii) The two oars are parallel
consecutive interior angle theorem:
If a transversal cuts through two line and the consecutive interior angles are supplimentary, then the two lines are parallel
in a single power what is the answer to the following:
5 to the power of 3 divided by 5 ?
3 to the power of 6 divided by 3 ?
Answers
Answer:
a-25
b-243
5^3 = 125/3 = 25
3^6 = 729/3 = 243
125/5=25
3x3x3x3x3x3=729
729/3=243
Need to solve for x
X+6=2x+5
Answers
Answer:
x=1
Step-by-step explanation:
x+6=2x+5
move the x to the right-hand side, and the 5 to the left-hand side (the sign will also change from a + to a -
6-5=2x-x
therefore, you will get:
x=1
Answer:
Step-by-step explanation:
x = 1
x + 6 = 2x + 5
6 - 5 = 2x - x
-1 = x
x = 1
--------------
check
1 + 6 = 2 × 1 + 5 (remember pemdas)
7 = 7
the answer is good
If s(x) = 2x² and f(x) = 3x, which value is equivalent to (s-f)(-7)?
O-439
O-141
O 153
O 443
Answers
The value of expression (s - f) (- 7) would be,
⇒ (s - f) (- 7) = 119
We have to given that,
Functions are defined as,
⇒ s (x) = 2x²
⇒ f (x) = 3x
Now, We can find the value of (s - f) (- 7) is,
⇒ (s - f) (- 7)
⇒ s (- 7) - f (- 7)
⇒ 2 (- 7)² - (3 × - 7)
⇒ 2×49 + 21
⇒ 98 + 21
⇒ 119
Therefore, The value of expression (s - f) (- 7) would be,
⇒ (s - f) (- 7) = 119
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ1
A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation?
VX
O(x, y) - (x + 5, y-3)
O(x,y) → (x + 5, y + 3)
(x, y) (x-3, y + 5)
O(x,y) → (X + 3, y + 5)
Answers
Answer:
Step-by-step explanation:
5 units up means y is crease by y =>
y+5
and x unit left means x is decreasedby 3
=> x-3
thus new coordinates are (x-3,y+5)
Thus (x,y) → (x − 3, y + 5) (x, y) is
correct
P.S. have a wonderful weekend!!
Angle ADB and CD are straight lines. angle ADC = 5 x angle CDB Work out the size of angle ADC.
Answers
Answer:
Step-by-step explanation:
Solve for j I will give brainlest anwser
(h-4) / j = k
Answers
Answer:
j=h-4/k this is the answer if you are solving for j
Step-by-step explanation:
If a ∥ b and b ⊥ y, then _____
Answers
Answer:
a ⊥ y
Step-by-step explanation:
since b is parallel to a & perpendicular to y , line y will eventually cut across line a at a 90 degree angle as well
Answer:
a ⊥ y
Step-by-step explanation:
Look at the image given below.
differenciate the Function 1/ X3
Answers
Step-by-step explanation:
To differentiate the function f(x) = 1/x^3, we can use the power rule of differentiation. Here's the step-by-step process:
Write the function: f(x) = 1/x^3.
Apply the power rule: For a function of the form f(x) = x^n, the derivative is given by f'(x) = nx^(n-1).
Differentiate the function: In our case, n = -3, so the derivative is:
f'(x) = -3 * x^(-3-1) = -3 * x^(-4) = -3/x^4.
Therefore, the derivative of the function f(x) = 1/x^3 is f'(x) = -3/x^4.
Variability ? I'm confused
Answers
Gasoline at a particular gas station costs $2.78 per gallon. If Cory buys $18 of gas, how many gallons did he buy?
Answers
Answer:
Cory bought 6.474 gallons of gasolline.
Step-by-step explanation:
The total cost of gasoline (\(C\)), measured in dollars, is given by the following expression:
\(C = n\cdot c\)
Where:
\(n\) - Amount of gasoline, measured in gallons.
\(c\) - Unit cost, measured in dollars per gallon.
Given that \(C = \$\,18\) and \(c = \$\,2.78\,\frac{1}{gal}\), the amount of gasoline is cleared and calculated:
\(n = \frac{C}{c}\)
\(n = \frac{\$\,18}{\$\,2.78\,\frac{1}{gal} }\)
\(n = 6.474\,gal\)
Cory bought 6.474 gallons of gasolline.