Practice Final

# Practice Final - Stat 116 Practice Final 1 Let X1 0 410 X2...

This preview shows pages 1–2. Sign up to view the full content.

Stat 116 Practice Final 1. Let X 1 X 2 X 3 Normal 0 0 1 , 4 1 0 1 1 0 0 0 9 (1) Find f X 1 | X 2 ,X 3 ( X 1 | X 2 = 1 , X 3 = 5) (2) Let Y 1 = X 1 + X 2 , Y 2 = X 1 /X 2 . Find the joint p.d.f. of Y 1 , Y 2 : f Y 1 ,Y 2 ( y 1 , y 2 ). 2. Suppose the volume of a raindrop ( V i ) can be modeled as a Gamma distribution with parameter p = 2, λ = 16 (i.e. V i Gamma(2,16), E ( V i ) = 2 / 16). (1) Find the moment generating function (MGF) of the total volume of N raindrops where N is a ﬁxed number (i.e. The MGF of V = Σ N i =1 V i ). (2) Now let N be a random variable with a Poisson distribution with parameter λ = 100. Find E ( V ) and V ar ( V ). (3) What is the moment generating function of V when N Pois(100) (A random sum of random variables)? 3. Let X and Y be independent random variables with X Gamma( r, 1) and Y Gamma( s, 1). Let Z 1 = X + Y and Z 2 = X/ ( X + Y ). (1) Find the joint distribution of

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

Practice Final - Stat 116 Practice Final 1 Let X1 0 410 X2...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online