Question

1)Suppose E(x)=3 and Var(x)=4. Compute E(Y) and Var(Y) when

Y=3X+2

Y=-5X+4

2)Suppose that a large number of containers of candy are made up of two types, say A and B. Type A contains 70% sweet and 30% sour ones while for type those percent’s are reversed. Furthermore, suppose that 60% of all candy jars are of type A, while the remain are of type B. If you are given a jar of unknown type and draw one pieces of candy;

What is  the probability that it is type A given that it sweet?

What is the probability that it is type B given that it sweet?

Answer 1

(1) Given, E(X)=3, Var(X)=4

case 1: when $Y=3X+2$

$E(Y)=3E(X)+2=3(3)+2=11\\ Var(Y)=3var(Y)+0=3(4)+0=12$

case 2: When $Y=-5x+4$

$E(Y)=-5E(X)+4=-5(3)+4=-11 \\ Var(Y)-5var(X)+0=-5(4)=-20$

(2) Probability that it is type A given that it sweet=

$\dfrac{ \text{ Number of candies of type A}}{\text{ No. of sweet candies of type A}}=\dfrac{60}{70}=0.857$

probability that it is type B given that it sweet

=$\dfrac{ \text{ Number of candies of type B}}{\text{ No. of sweet candies of type B}}=\dfrac{30}{40}=0.75$