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section 3

# section 3 - a What is the pmf and b What is the cdf c Graph...

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Random variables A quantity whose value depends on the result of a random experiment A function that assigns a numerical value to every outcome in the sample space of a random experiment A random variable X is called discrete if its possible values form a discrete set. This means that if we arrange all possible values of X in order, then there is a gap between each value and the next one. The probability mass function (pmf) and the cumulative distribution function (cdf) F(x) = ( ) p y Example: 2 fair dice are tossed independently. Let M= maximum of the two tosses
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Unformatted text preview: a. What is the pmf and b. What is the cdf c. Graph the cdf a. Possible values of M are {1,2,3,4,5,6} P(1) = P(M=1) = 1/36 P(2) =p(M=2) = p(2,1) + p(1,2) + p(2,2)= 3/36 P(3) = 5/36 P(4)= 7/36 P(5)= 9/36 P(6)= 11/36 b. Cdf is the summation of probabilities c. Graph is the function y= x 2 The expected value of a discrete r.v X is E(X)= ( ) x p x The variance is V(x)= ( - ) ( ) x u 2p x Frequently used distribution P(1)= q P(0) = 1-q E(X) = nq V(X)= nq(1-q)...
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