The weight of apples selected at random from a bin at the local supermarket is a

ID: 3356218 • Letter: T

Question

The weight of apples selected at random from a bin at the local supermarket is a random

variable X with mean 5 oz. and standard deviation 1.5 oz. Suppose we pick 2 apples from

the bin at random and put them in a bag. Suppose the price of apples is 0.2 dollars per oz.

Let the random variable W = price of the bag of apples.

(i) Write the random variable W in terms of the weight of the 2 randomly selected

apples X1 and X2. Answer: W=0.2(X1 + X2)

(ii) What is E(W)? Answer: 2

(iii) What is Var(W)? Answer: 0.18

I have the correct answers but could you explain question 3??

Thanks!

(1) here price of apples =0.2*(weight of first +weight of second)

W =0.2*(X1+X2)

(ii) E(W)=0.2*(E(X1)+E(X2)) =0.2*(5+5)=2

(iii)Var(W)= 0.22 *(Var(X1)+Var(X2)) =0.04*(1.52+1.52) =0.04*(2.25+2.25)=0.04*4.5=0.18

please reply if you need further explanation

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