# 7-5 - 7-5 Random Variables Probability Distributions...

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7-5 Random Variables, Probability Distributions, Expected Value R ANDOM VARIABLES Experiment: flip a coin twice Sample space: {HH, HT, TH, TT} Game: if we get HH or TT, I pay you \$1 if we get TH, you pay me \$2 if we get HT, I pay you \$.50 assign a numerical value X to each outcome: outcome X (my earnings) HH -1 HT -.50 TH 2 TT -1 X is called a random variable (r.v. for short) A random variable is an assignment of a real number to each outcome of a sample space 7-5 p. 1

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if we define a r.v. X on a sample space it makes sense to talk about the probability of various values of the r. v. X, as opposed to the probability of outcomes : P(X = -1) = ½ P(X = -.5) = ¼ P(X = 2) = ¼ can describe the probabilities using functional notation call our function p : p (-1) = ½ p (-.5) = ¼ p (2) = ¼ p is called the probability function or probability distribution of random variable X it is often useful to graph the probability distribution here we show the graph in histogram form: 7-5 p. 2 1 .5 x -1 -.5 2.0 p(x)
E XPECTED V ALUE

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