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Random Variables Notes Spring

Random Variables Notes Spring - 2 of 7 1.2 Probability...

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2 of 7 1.2 Probability distributions Types of questions we want to answer “Find the probability that the mean is . . . ” english statement mathematical notation “equal to fifty” P ( μ = 50) “not equal to fifty” P ( μ 6 = 50) “not fifty” P ( μ 6 = 50) “greater than fifty” P ( μ > 50) “at least fifty” P ( μ 50) “less than fifty” P ( μ < 50) “no more than fifty” P ( μ 50) “between forty and fifty” (inclusive) P (40 μ 50) “between forty and fifty” P (40 < μ < 50) 1.2 Probability distributions Probability distribution P ( x i ) . Definition 1.2 describes the probability of a discrete random variable x . P ( x i ) is the probability of observing x i . Describes population . Two key properties of probability distributions k X i =1 P ( x i ) = 1 (1) with k possible values of x . 0 P ( x i ) 1 , for i = 1 , 2 , . . . , k (2) Ways we can represent P ( x i ) Three basic ways we can represent P ( x i ). 1. Table x P(x) 0 0.03125 1 0.15625 2 0.31250 3 0.31250 4 0.15625 5 0.03125 2. Probability distribution plot Anthony Tanbakuchi MAT167

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Random variables 3 of 7 0 1 2 3 4 5 0.05 0.15 0.25 x P(x) 3. Probability histogram
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Random Variables Notes Spring - 2 of 7 1.2 Probability...

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