Please do 4.53 and 4.57 Find E(X) and E(X2) and then, using these values, evalua

Question

Please do 4.53 and 4.57

Find E(X) and E(X2) and then, using these values,
evaluate E[(2X + 1)2].

4.53 Referring to Exercise 4.35 on page 127, find the mean and variance of the discrete random variable Z = 3X-2, when X represents the number of errors per 100 lines of code. tributor equal to three-fourths of the wholesale price. If the probability distribution of the random variable X, the number of cartons that are sold from this lot, is 0 123 4 5 4.54 Using Theorem 4.5 and Corollary 4.6, find the mean and variance of the random variable Z 5X + 3 where X has the probability distribution of Exercise 4.36 on page 127 f(T) 13 1 11 find the expected profit. 4.56 Repeat Exercise 4.43 on page 127 by applying Theorem 4.5 and Corollary 4.6 4.55 Suppose that a grocery store purchases 5 car tons of skim milk at the wholesale price of 1.20 per carton and retails the milk at $1.65 per carton. After the expiration date, the unsold the shelf and the grocer receives a credit from the dis 4.57 Let X be a random variable with the following milk is removed from probability distribution: )3

Explanation / Answer

Ans:

4.57)

E(X)=-3*(1/6)+6*(1/2)+9*(1/3)

=-0.5+3+3=6-0.5=5.5

E(X)=5.5

E(X2)=(-3)2*(1/6)+62*(1/2)+92*(1/3)=(9/6)+(36/2)+(81/3)=1.5+18+27=46.5

E[(2X+1)2]=E[4X2+1+4X]=4E(X2)+1+4E(X)=4*46.5+1+4*5.5=186+1+22=209

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