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Probability Distributions: DRV

The probability distribution of a random variable is a listing of the possible values of the variable and the corresponding probabilities. This is usually written in a table. Probability Distributions: DRV. This is a probability distribution. Important properties of a probability distribution.

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Probability Distributions: DRV

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  1. The probability distribution of a random variable is a listing of the possible values of the variable and the corresponding probabilities. This is usually written in a table. Probability Distributions: DRV This is a probability distribution Important properties of a probability distribution Total probability adds to 1. ∑pi 1 Probability is always positive. pi  0

  2. Example 1 X is a discrete random variable with distribution given by the table below. Find the value of c. Probability Distributions: DRV 0.1 + 0.3 + c + 0.2 = 1 Give c = 0.4

  3. Example 2 The probability distribution of a random variable X is given by P(X = x) = kx for x = 1, 2, 3, 4, 5. Find k and P(X > 3). Probability Distributions: DRV 15k = 1 k = 1/15 P(X > 3) = 9/15 = 3/5

  4. Mean  E(X) ∑x. P(X  x) E(X) is the ‘expectation of X’ Mean and Variance : DRV Variance  Var(X) 2 E(X2) – [E(X)]2 where E(X2)  ∑x2 .P(X  x) Standard deviation  =Var(x)

  5. Example 1 A random variable X can take the values indicated in the table below. Calculate the mean and variance of X. Mean and Variance : DRV The mean  E(X)  1.5 Var(X)  E(X2) – [E(X)]2 3.7 – 1.52 1.45

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