Discrete Probability Distributions. Random Variables. Expected Value (mean, average). Μ = E(X) = Σ value(x) x probability(x). Expected value = 0.5 x (-1) + 0.5 x (+1) = 0. Example: Lottery of 1,000 tickets, with the following payout structure, has an E(x) = $1.00.
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Μ = E(X) = Σ value(x) x probability(x)
Example: Lottery of 1,000 tickets, with the following payout structure, has an E(x) = $1.00.
Var(Y) = s2 = Σ[(y – E(Y))2 x P(y)]
Or Var(Y) = s2 = Σ[P(y) x Y] – E(Y)2
Sdev s = (s2)0.5
n! = n x (n – 1) x (n – 2) …. x 1
Example: 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720.
Example: a die is rolled exactly n = 5 times. What is the probability of rolling exactly x = 2 sixes? (Note the probability of rolling a 6 is P(six) = 1/6 = 0.166667.)
Or, using MS Excel, go to Formulas/More Functions/Statistical/BINOMDIST
Mean = np
Variance = np(1 – p)