{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 06_26_2 - X Y be 29 ≤ ≤ ≤ ≤ ≤ = otherwise 1 1 1...

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

STAT 410 Examples for 06/26/2009 Summer 2009 2.3 Conditional Distributions. 1. Consider the following joint probability distribution p ( x , y ) of two random variables X and Y: y x 0 1 2 p X ( x ) 1 0.15 0.15 0 0.30 2 0.15 0.35 0.20 0.70 p Y ( y ) 0.30 0.50 0.20 f) Find the conditional probability distributions p X | Y ( x | y ) = ( 29 ( 29 y p y x p , Y of X given Y = y , y = 0, 1, 2. x p X | Y ( x | 0 ) x p X | Y ( x | 1 ) x p X | Y ( x | 2 ) 1 0.15 / 0.30 = 0.50 1 0.15 / 0.50 = 0.30 1 0.00 / 0.20 = 0.00 2 0.15 / 0.30 = 0.50 2 0.35 / 0.50 = 0.70 2 0.20 / 0.20 = 1.00 g) Find the conditional probability distributions p Y | X ( y | x ) = ( 29 ( 29 x p y x p , X of Y given X = x , x = 1, 2. y p Y | X ( y | 1 ) y p Y | X ( y | 2 ) 0 0.15 / 0.30 = 0.50 0 0.15 / 0.70 = 3 / 14 1 0.15 / 0.30 = 0.50 1 0.35 / 0.70 = 7 / 14 2 0.00 / 0.30 = 0.00 2 0.20 / 0.70 = 4 / 14

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

View Full Document
2. Let the joint probability density function for
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ( X , Y ) be ( 29 ≤ + ≤ ≤ ≤ ≤ = otherwise 1 , 1 , 1 24 , y x y x y x y x f Recall: f X ( x ) = ( 29 2 1 12 x x-, 0 < x < 1. f Y ( y ) = ( 29 2 1 12 y y-, 0 < y < 1. f Y | X ( y | x ) = ( 29 ( 29 x f y x f , X = ( 29 2 1 2 x y-, 0 < y < 1 – x , 0 < x < 1. P ( Y > 1 / 3 | X = 1 / 2 ) = ( 29 ∫ 2 1 3 1 2 2 1 2 dy y = ∫ 2 1 3 1 8 dy y = 9 5 . P ( Y > 1 / 4 | X = 1 / 3 ) = ( 29 ∫ 3 2 4 1 2 3 2 2 dy y = 64 55 . f X | Y ( x | y ) = ( 29 ( 29 y f y x f , Y = ( 29 2 1 2 y x-, 0 < x < 1 – y , 0 < y < 1. P ( X < 1 / 2 | Y = 1 / 3 ) = ( 29 ∫ 2 1 2 3 2 2 dx x = 16 9 = 0.5625....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

06_26_2 - X Y be 29 ≤ ≤ ≤ ≤ ≤ = otherwise 1 1 1...

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

View Full Document
Ask a homework question - tutors are online