The random variable Y has normal distribution with a mean of 30 and a variance of 16, i.e. Y~ N(30, 16). Let T = Y+3. Compute E(T) and Var(T). What is the distribution of T? (As problem 1 shows, in general knowing the expected value and variance doesn't mean that we know the distribution, but when Y is normal, T will be normal as well ·cu
The random variable Y has normal distribution with a mean of 30 and a variance of 16, i.e. Y~ N(30, 16). Let T = Y+3. Compute E(T) and Var(T). What is the distribution of T? (As problem 1 shows, in general knowing the expected value and variance doesn't mean that we know the distribution, but when Y is normal, T will be normal as well ·cu
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Show full answers and steps to part b) c) & d)
Please don’t use R or excel formula. Use actual number from the normal distribution table and show how to get to that answer
![[10] The random variable Y has normal distribution with a mean of 30 and a variance
of 16, i.e. Y~ N(30, 16). Let T = Y+3.
a) Compute E(T) and Var (T). What is the distribution of T? (As problem 1
shows, in general knowing the expected value and variance doesn't mean that
we know the distribution, but when Y is normal, T will be normal as well
because T is basically scaling and then shifting Y so its shape is not going to
change. Indeed, the standard Z-transformation does something similar.)
b) Can you compute the following probability P(8.5 ≤ T ≤ 10)? Explain why.
c) Compute P(T > 21)?
d) Compute P(14≤ T ≤ 20)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3574180-5be7-46af-9f18-c1fbb9ec682c%2F68385cc8-79ed-4480-9b7a-44901f9a978b%2F4focju6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[10] The random variable Y has normal distribution with a mean of 30 and a variance
of 16, i.e. Y~ N(30, 16). Let T = Y+3.
a) Compute E(T) and Var (T). What is the distribution of T? (As problem 1
shows, in general knowing the expected value and variance doesn't mean that
we know the distribution, but when Y is normal, T will be normal as well
because T is basically scaling and then shifting Y so its shape is not going to
change. Indeed, the standard Z-transformation does something similar.)
b) Can you compute the following probability P(8.5 ≤ T ≤ 10)? Explain why.
c) Compute P(T > 21)?
d) Compute P(14≤ T ≤ 20)?
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