Lecture13_14(09-24_26-2008)

# Lecture13_14(09-24_26-2008) - 36-225 Handout for Lectures...

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: 36-225 - Handout for Lectures # 13 & 14September 24 & 26, 2008Special Discrete Random Variables (Distributions)I. The Binomial Random Variable (Distribution)Consider an experiment which consists of n independent (Bernoulli) trials, each hav-ing two possible outcomes (Success or Failure), and each having P(Success) =p.Let the RV Y be the number of successes (out of n).Y is said to be a binomial random variable, and we write:•PY(y) =P(Y=y) =nypy(1-p)n-yy=1,2, . . . ,n•E(Y) =np•V(Y) =np(1-p)II. The Geometric Random Variable (Distribution)Consider asequenceof independent Bernoulli trials, all having the same P(Success)=p.Define:Y - the number of trials until the first success.We say thatYis ageometricrandom variable, and we write:Example: Toss a fair coin repeatedly, and letYbe the number of tosses (trials) untilthe first “H”.=⇒Y∼Geom(p= 1/2).IfY∼Geom(p), what is the probability distribution ofY,PY(y)?...
View Full Document

{[ snackBarMessage ]}

### Page1 / 8

Lecture13_14(09-24_26-2008) - 36-225 Handout for Lectures...

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

View Full Document
Ask a homework question - tutors are online