Show that the standard score of the sample mean X, is equal to Y. Show that the mean and variance of the random variable y are 0 and 1, respectively. iii) iii) Show using the moment generating function technique that Y is a standard normal random variable. i) ii)
Show that the standard score of the sample mean X, is equal to Y. Show that the mean and variance of the random variable y are 0 and 1, respectively. iii) iii) Show using the moment generating function technique that Y is a standard normal random variable. i) ii)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
Related questions
Question
Number A...
![PAGE LAYOUT
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Font
A
REFERENCES MAILINGS
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A
i)
11)
▾
EE
i)
E-25 E* T AaBbCc AaBbCc AaBbC AaBbCcL AaB AaBbcct AaBb
T Normal
1 No Spac... Heading 1 Heading 2
Subtitle
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REVIEW
Paragraph
√n
VIEW
a)
Let X1, X2, X3, Xn be a random sample of size n from population X. Suppose that X~N(0, 1)
and y =
-√n.
Show that the standard score of the sample mean x, is equal to Y.
Show that the mean and variance of the random variable y are 0 and 1, respectively.
III)
iii) Show using the moment generating function technique that Y is a standard normal
random variable.
Styles
Title
iv) What is the probability that Y² is between 0.02 and 5.02?
b)
Let X1, X2, X and Y₁, Y₂,..., Ym be random samples from populations with moment generating
functions Mx:(t) = e³t-¹2 and My(t)
(2)
respectively
Find the sampling distribution of the statistic W = X₁ + 2X2 X3 + X+ + Xs.
ii) What is the value of the sample size , if PI (X-X)²> 68.3392] = 0.025?
iii) What is the value of the sample size if P(Y-ur210) < 0.04?
23](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F283af5c3-8e1d-42a7-83bf-b44908929c9c%2F978897fa-24f7-40a2-8393-962e5e242d87%2Flrs15ik_processed.jpeg&w=3840&q=75)
Transcribed Image Text:PAGE LAYOUT
-AA
Font
A
REFERENCES MAILINGS
Aa -
aly -
A
i)
11)
▾
EE
i)
E-25 E* T AaBbCc AaBbCc AaBbC AaBbCcL AaB AaBbcct AaBb
T Normal
1 No Spac... Heading 1 Heading 2
Subtitle
Subtle
REVIEW
Paragraph
√n
VIEW
a)
Let X1, X2, X3, Xn be a random sample of size n from population X. Suppose that X~N(0, 1)
and y =
-√n.
Show that the standard score of the sample mean x, is equal to Y.
Show that the mean and variance of the random variable y are 0 and 1, respectively.
III)
iii) Show using the moment generating function technique that Y is a standard normal
random variable.
Styles
Title
iv) What is the probability that Y² is between 0.02 and 5.02?
b)
Let X1, X2, X and Y₁, Y₂,..., Ym be random samples from populations with moment generating
functions Mx:(t) = e³t-¹2 and My(t)
(2)
respectively
Find the sampling distribution of the statistic W = X₁ + 2X2 X3 + X+ + Xs.
ii) What is the value of the sample size , if PI (X-X)²> 68.3392] = 0.025?
iii) What is the value of the sample size if P(Y-ur210) < 0.04?
23
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