practice_midterm2

# practice_midterm2 - STAT 230 Introduction to Probability...

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

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.

Unformatted text preview: STAT 230 Introduction to Probability and Random Variables Summer 2009 Practice for Midterm 2 Exercise Let X be the number of fish caught by a fisherman in one afternoon. Suppose that X is distributed Poisson ( λ ) . Each fish has probability p of being a salmon independently of all other fish caught. Let Y be the number of salmon caught. Show that Y is Poisson ( p λ ) . ( ) ( | ) ( ) (1 ) ! (1 ) ! ! (1 ) !( )! ! (1 ) 1 (1 ) ! ( )! (1 ) x y x y x y x y x y x y x y x y x y x y y y x x x y y y P Y y P Y y X x P X x x p p e y x x p p e y x x p p y x y x p p e p y x y p p y λ λ λ λ λ λ λ ∞ = ∞ − − = ∞ − − = ∞ − = − ∞ − = − = = = = =      = − ×               = − ×             = − ×   −      − = − ×   −   − = ∑ ∑ ∑ ∑ ∑ (1 ) 1 (1 ) ! !...
View Full Document

• Fall '08
• unknown
• Probability distribution, Probability theory, probability density function, Probability mass function, Random Variables Summer

{[ snackBarMessage ]}

### Page1 / 3

practice_midterm2 - STAT 230 Introduction to Probability...

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

View Full Document
Ask a homework question - tutors are online