Practice - Problem 3 If X , ...,X n are independent with...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
OR 3500/5500, Summer’08 Practice Problems Not to be turned in. Problem 1 You have a fair coin and you keep tossing it until you get 5 heads. (a) Find the probability that you will need to toss the coin exactly 20 times. (b) If X is the random variable which denotes the number of times you need to toss the coin to get k heads, find the probability mass function of X . Problem 2 Find the probability that a poker hand of 5 cards will contain no card smaller than 7, given that it contains at least 1 card over 10(Ace is the highest card).
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Problem 3 If X , ...,X n are independent with means and variance 2 , then nd E h n X i =1 ( X i- X n ) 2 i . Problem 4 If X Gamma ( , ). Find E ( X k ) ,k 1 . Problem 5 If X and Y are independent N (0 , 1), show that P [ X 2 + Y 2 8] 1 8 . (Given: E ( X 4 ) = 3) Problem 6 Boxes and balls again!!! Suppose n balls are thrown randomly into n boxes. Find the probability that only box 1 is empty. 1...
View Full Document

Ask a homework question - tutors are online