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STAT 2507A &acirc;€“ Week 4 - June 8

# STAT 2507A &acirc;€“ Week 4 - June 8 -...

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1 STAT 2507A – Week 4 –  June 8 Jerry Situ 5.1-5.2 Summery 2009

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Exercise What is: 1) P(X=b) 2) P(Y=r|X=c) 3) P(Y=q) 4) P(X=a   Y=q) 5) P(X=c|Y=p) 6) P(X=a U Y=q) 2
Exercise What is: 1) P(X=b) 2) P(Y=r|X=c) 3) P(Y=q) 4) P(X=a   Y=q) 5) P(X=c|Y=p) 6) P(X=a U Y=q) X a b c Tota l Y p .05 .4 .05 .5 q .05 .15 .10 .3 r 0 .15 .05 .2 Total .1 .7 .2 1 3

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Review: Working with discrete  random variable Given the follow probability distribution: Things to notice: X may take values 0,1,2,3,4 ONLY P(X=x) for all x is equal to 1. 4 x 0 1 2 3 4 p(x) .2 .1 .4 .25 .05
Review (2) Calculate  µ  and  σ : σ 2 =VAR(X)=  Σ (x 2 p(x)) -  µ =4.75-1.85 2 =1.3275  = 1.15 (by taking square root of  σ σ 2) 5 x p(x) xp(x) x 2 p(x) 0 .2 0 0 1 .1 .1 .1 2 .4 .8 1.6 3 .25 .75 2.25 4 .05 .2 .8 Total: 1 1.85  [this is  µ  =E(X)] 4.75 (Red numbers are given)

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Binomial Distribution(1) We consider an experiment with only two possible  results («success» and «failure»). The probability of  success is  (the probability of failure 1 -p ) Suppose  that
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STAT 2507A &acirc;€“ Week 4 - June 8 -...

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