Question

if X1, X2 have the joint pdf f(x1, x2) = 4x1(1-x2) ,     0<x1<1 0<x2<1 and...

  1. if X1, X2 have the joint pdf f(x1, x2) = 4x1(1-x2) ,     0<x1<1 0<x2<1

and 0,                  otherwise

1- Find the probability P(0<X1<1/3 , 0<X2<1/3)

2- For the same joint pdf, calculate E(X1X2) and E(X1 + X2)

3- Calculate Var(X1X2)

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

1.

2.

= 4 * (1/3) * (1/2 - 1/3)

= 2/9

= 4 (1/3 - 1/6 + 1/4 - 1/6)

= 1

3.

= 4 * (1/4) * (1/3 - 1/4)

= 1/12

Var(X1 X2) = E((X1 X2)2 ) - [E(X1 X2)]2

= 1/12 - (2/9)2

= 11 / 324

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