# lec15 - STATISTICS 13 Lecture 15 Review Random...

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STATISTICS 13 Lecture 15 Oct 29, 2010

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Review Random variables --definition --probability distribution -- mean and variance
Mean and Standard Deviation of a Discrete Random Variable Let X be a discrete random variable with probability distribution p(x) . Then the mean (expectation/expected value), variance and standard deviation of X are given by the following : (all the summation is taken over all possible values of X) 2 2 2 ) ( : deviation Standard ) ( ) ( ) ( : Variance ) ( ) ( : value) d on/expecte (expectati Mean X Sd x p x X Var x xp X E

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Example : Coin Toss (Cont.) X = number of heads in 3 tosses of a fair coin x p(x) xp(x) (x-  2 0 1/8 0 (-1.5) 2 (1/8)=0.28125 1 3/8 3/8 (-0.5) 2 (3/8)=0.09375 2 3/8 6/8 (0.5) 2 (3/8)=0.09375 3 1/8 3/8 (1.5) 2 (1/8)=0.28125 sum 1
Probability Calculation Toss a fair coin three times, what is probability that we observe fewer than two heads? Answer: What is the probability that we observe more than one heads? Answer:

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Binomial Random Variables A binomial experiment consists of n identical trials The trials are independent to each other Each trial has only two outcomes : coded as “success” and “failure” P(success) = 1-P(failure)=p, where 0 < p < 1 X = number of successes; then X is a binomial random variable with parameters n and p, denoted by X~ Binomial (n, p) . We also say X has a Binomial (n, p) distribution
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## This note was uploaded on 11/18/2010 for the course STA 80760 taught by Professor Jiepeng during the Spring '10 term at UC Davis.

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lec15 - STATISTICS 13 Lecture 15 Review Random...

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