stat400lec9 - Probability of success p Probability of...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Statistics 400 Section 3.2 3.3 Expected value and Bernoulli Trials Review: Expected value of u(X) E[u(X)]= ) ( ) ( x f x u =u(x1)*f(x1)+u(x2)*f(x2)+ …+ u(xk)*f(xk) Example: Let X has p.m.f f(x)= 10 x , x=1,2,3,4 Calculate E[X], E[X 2 ] and E[X(5-X)] Ping Ma Lecture 9 Fall 2005 - 1 -
Background image of page 1

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

View Full DocumentRight Arrow Icon
Properties of Mathematical Expectation (a) E[c]=c if c is a constant. (b) E[cu(X)]=cE[u(X)] (c) E[c1*u1(X)+c2*u2(X)]=c1*E[u1(X)]+c2*E[u2(X)] Mean: ] [ X E = μ Variance: ] ) [( 2 2 σ - = X E = ] 2 [ 2 2 + - X X E Let X be the outcome when rolling a fair die. Calculate mean and variance of X. Ping Ma Lecture 9 Fall 2005 - 2 -
Background image of page 2
Let r be a positive integer, E[X r ]= ) ( x f x r is called rth moment of the distribution about the origin. E[(X-b) r ]= - ) ( ) ( x f b x r is called rth moment of the distribution about b. Bernoulli Experiment: A Bernoulli experiment is a random experiment, the outcome of which can be classified as success and failure. Example : tossing a coin
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Probability of success p Probability of failure q=1-p. Let X be random variable of Bernoulli distribution. Outcome Success 1 Failure Probability p q=1-p X can take value of either 0 or 1 Notation: X ~ Ber (p) Setting: 1. Each observation falls into one of two categories: Success or Failure 2. P (Success) = p Probability mass function is f(x)= Ping Ma Lecture 9 Fall 2005 - 3 -Expected value Variance A sequence of Bernoulli Trials: A sequence of Bernoulli experiments are conducted independently and the probability of success (p) remains the same. Example: For a million of instant lottery tickets, suppose that 205 are winner, If 5 tickets are purchased, what is the probability we have (0,0,0,1,0) Ping Ma Lecture 9 Fall 2005 - 4 -Ping Ma Lecture 9 Fall 2005 - 5 -...
View Full Document

This note was uploaded on 07/24/2008 for the course STAT 400 taught by Professor Tba during the Fall '05 term at University of Illinois at Urbana–Champaign.

Page1 / 5

stat400lec9 - Probability of success p Probability of...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online