{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# note09 - Chapter 4 Section 4 Geometric Distribution Page...

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: Chapter 4 Section 4: Geometric Distribution Page 232-233 • You have a Bernoulli experiment, except you only sample until you get your first success. • X = the number of trials needed until you get the first success. • Notation: X ∼ Geom( p ) where p is the probability of success pmf for the Geometric Distribution f ( x ) = p (1- p ) x- 1 for x = 1 , 2 , 3 , . . . otherwise cdf for the Geometric Distribution F ( x ) = P ( X ≤ x ) = 1- (1- p ) x Mean and Variance of Geometric Distribution • Mean: E( X ) = ∑ for all x xf ( x ) = 1 p • Variance: Var( X ) = ∑ for all x x 2 f ( x )- μ 2 = 1- p p 2 Ex. A particularly biased coin, when tossed, will come up heads 75% of the time. Assume that trials are independent. Let X = the number of the tosses that results in the first head. (a) What is the pmf of X ? (b) Find the probability that exactly three trials are required to get the first head....
View Full Document

{[ snackBarMessage ]}

### Page1 / 5

note09 - Chapter 4 Section 4 Geometric Distribution Page...

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

View Full Document
Ask a homework question - tutors are online