100AHW4 - Problem 5: Suppose we divide the time axis into...

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

View Full Document Right Arrow Icon
STAT 100A HWIV Due next Wed in class Problem 1: For Z Bernoulli( p ), calculate E[ Z ]. Problem 2: For X Binomial( n,p ), calculate E[ X ]. Problem 3: For X Geometric( p ), calculate E[ X ]. Problem 4: Suppose we have a five-letter alphabet, A, B, C, D, E, and their probabilities are p ( A ) = 1 / 4, p ( B ) = 1 / 4, p ( C ) = 1 / 4, p ( D ) = 1 / 8, p ( E ) = 1 / 8. (1) Design a scheme for generating a letter according to the above distribution by coin flipping. (2) Calculate the expected number of coin flippings for generating a letter according to the above distribution. (3) Argue that your coin flipping scheme leads to a prefix coding of the five letters.
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 5: Suppose we divide the time axis into small periods (0 , t ), ( t, 2 t ), . .. Within each period, we ip a coin independently. The probability of getting a head is t . (1) Let X be the number of heads within the interval [0 ,t ]. Calculate the limit of P ( X = k ) as t 0, for k = 0 , 1 , 2 ,... . Also calculate E[ X ]. (2) Let T be the time until the rst head. Calculate the limit of P ( T > t ) as t 0. In both (1) and (2), let us assume that t is a multiple of t . 1...
View Full Document

This note was uploaded on 01/29/2010 for the course STATS 100A 262303210 taught by Professor Wu during the Fall '09 term at UCLA.

Ask a homework question - tutors are online