Top left conditional pmf of x given the rst coin is

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

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

Unformatted text preview: Example 2.10.2 Consider a two stage experiment. First roll a die, and let X denote the number showing. Then flip a fair coin X times, and let Y denote the total number of times heads shows. Find P {Y = 3} and P (X = 3|Y = 3). Solution: By the law of total probability, 6 P {Y = 3} = P (Y = 3|X = j )pX (j ) j =1 = = = 1 0+0+ 6 1 0+0+ 6 1 . 6 3 −3 4 −4 5 −5 6 −6 2+ 2+ 2+ 2 3 3 3 3 1 1 10 20 ++ + 8 4 32 64 50 CHAPTER 2. DISCRETE-TYPE RANDOM VARIABLES Now P {X = 3, Y = 3} is the term in the above sum for j = 3: P {X = 3, Y = 3} = Therefore, P {X = 3, Y = 3} 1 P (X = 3|Y = 3) = =. P {Y = 3} 8 2−3 6 = 1 48 . Example 2.10.3 Consider two boxes as shown in Figure 2.9. Box 1 has three black and two white Box 1 Box 2 Figure 2.9: Initial state of boxes. balls, while Box 2 has two black and two white balls. Consider the following two step experiment. Step 1: Select a ball from Box 1, all five having equal probability, and transfer it to Box 2. Step 2: Remove a ball from Box 2, with each of the five balls having the same chance of being removed. Define the following two events: W=“the ball that is transferred is white...
View Full Document

This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Tech.

Ask a homework question - tutors are online