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3.2 Explain how you would find the moment-generating function for an exponential-distributed random variable and how you can use the moment-generating function found to find E(Y) and V (Y).

3.2 Explain how you would find the moment-generating function for an exponential-distributed random variable and how you can use the moment-generating function found to find E(Y) and V (Y).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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3.2 Explain how you would find the moment-generating function for an exponential-distributed random variable and how you can use the moment-generating function found to find E(Y) and V(Y). 3.3 Solve the below problem: A manufacturing plant uses a specific bulk product. The amount of product used in one day can be modelled by an exponential distribution with B = 2 (measurements in tons). Find the probability that the plant will use more than 2 tons on a given day. Interpret your answer. 3.4 Complete the below statements. When a normal random variable Y is transformed to a standard normal random variable Z, the 3.4.1 value of Z is 1 and 3.4.2 value is 0. The probability density function for a standard normal random variable is f(z) = 3.4.3 3.5 Suppose that Y possesses the density function S2(2 – y), 0 < y< 2 0, elsewhere fy) = with the mean = 2/3 and the variance = 2/9. Using we find that: P(]Y - µl s 20) = P(Y -s 0.9428) = P(-.2761 < Y < 1.609).
Transcribed Image Text:3.2 Explain how you would find the moment-generating function for an exponential-distributed random variable and how you can use the moment-generating function found to find E(Y) and V(Y). 3.3 Solve the below problem: A manufacturing plant uses a specific bulk product. The amount of product used in one day can be modelled by an exponential distribution with B = 2 (measurements in tons). Find the probability that the plant will use more than 2 tons on a given day. Interpret your answer. 3.4 Complete the below statements. When a normal random variable Y is transformed to a standard normal random variable Z, the 3.4.1 value of Z is 1 and 3.4.2 value is 0. The probability density function for a standard normal random variable is f(z) = 3.4.3 3.5 Suppose that Y possesses the density function S2(2 – y), 0 < y< 2 0, elsewhere fy) = with the mean = 2/3 and the variance = 2/9. Using we find that: P(]Y - µl s 20) = P(Y -s 0.9428) = P(-.2761 < Y < 1.609).
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