stat400lec8 - Statistics 400 Lecture 8 (Sep 12) Random...

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Statistics 400 Lecture 8 (Sep 12) Random variables of the discrete type Review: Random Variable: (R.V.) is a variable whose value is a numerical outcome of a random phenomenon. Notation : X, Y, Z Discrete Random Variable: 1 A discrete R.V. has a coutable number of possible outcomes 2 These outcomes have a individual probabilities attached to them P(X= x )=f( x ) Probability Distribution: 1 Lists the values of X 2 Lists their respective probabilities (p.m.f) Value of X x 1 x 2 x 3 x 4 x 5 x k Probability mass function : f(x) f(x 1 ) f(x 2 ) f(x 3 ) f(x 4 ) f(x 5 ) f(x k ) Properties of p.m.f f(x) : (a) f(x)>0; ( b ) = 1 ) ( x f ; ( c ) P(X=x)=f(x). Bar graph
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(1) casting a fair die: 6 possible outcomes f(x)= x=1,2,3,4,5, 6. Uniform distribution: m possible outcomes have the same probability to appear. f(x)= x=1,2,3,…m . (2) There are 100 balls in a bag. 60 of them are white and rest are black. If we randomly draw 30 balls without replacement, what is the
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stat400lec8 - Statistics 400 Lecture 8 (Sep 12) Random...

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