Q3 Let X be a Normal random variable with mean 4, and variance o. A new random variable is defined as Y = aX +b where a and b are constants and a >0. By using the property that new random variable Y also has Normal probability density function, answer the following questions a) E[Y]=?, var(r)=? b) Suppose that 4g =0.5 and o = 4. Sketch fx (x) and fy(y) on the same figure for a = 2, b=1. Give the critical values on the figure. c) It is given that P(Xsc)= P(Y<3), find the value of c by using same constants and parameters given in part “b" (µx =0.5, o =4, a=2, b=1).

Q3 Let X be a Normal random variable with mean 4, and variance o. A new random variable is defined as Y = aX +b where a and b are constants and a >0. By using the property that new random variable Y also has Normal probability density function, answer the following questions a) E[Y]=?, var(r)=? b) Suppose that 4g =0.5 and o = 4. Sketch fx (x) and fy(y) on the same figure for a = 2, b=1. Give the critical values on the figure. c) It is given that P(Xsc)= P(Y<3), find the value of c by using same constants and parameters given in part “b" (µx =0.5, o =4, a=2, b=1).

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

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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