Suppose random variable has follwin probabilitydistribution X 1 3 5 P(X) 1/4 1/4

Question

Suppose random variable has follwin probabilitydistribution X           1         3        5 P(X)      1/4      1/4       1/2 I found the mean of x of X =3.5 and Variance (Sx)^2 of X=2.75 Question: A) define New random variable Y=3X+1. Use properties of meanof linear functions of random variables and your results inprevious problems(which i already found which is the mean anvariance) to find mean of Y B) Use properties of variance of linear functions of randomvariables to calculate variance and standard deviation of newrandom variable Y Suppose random variable has follwin probabilitydistribution X           1         3        5 P(X)      1/4      1/4       1/2 I found the mean of x of X =3.5 and Variance (Sx)^2 of X=2.75 Question: A) define New random variable Y=3X+1. Use properties of meanof linear functions of random variables and your results inprevious problems(which i already found which is the mean anvariance) to find mean of Y B) Use properties of variance of linear functions of randomvariables to calculate variance and standard deviation of newrandom variable Y

Explanation / Answer

We know that for any values a and b, E(aX+b) = aE(X) + b andthat Var(aX+b) = Var(aX) = (a^2)Var(X) a) E(Y) = E(3X+1) = 3E(X) + 1 = 3(3.5)+1 = 11.5 b) Var(Y) = Var(3X+1) = Var(3X) = (3^2)Var(X) = 9(2.75) =24.75

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