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