Mean of a Discrete Random Variable: Mean of a Discrete Random Variable μ = E(x) = ∑ x P(x) Expected value Mean The expected value is referred to the mean of a discrete random variable x and is denoted by E(x). The mean of a random variable X is μ.
A Step-by-Step Example: A Step-by-Step Example A men's soccer team plays soccer 0, 1, 2, or 3 days a week. The probability that they play 0 days is 0.38, the probability that they play 1 day is 0.27, the probability that they play 2 days is 0.15, and the probability that they play 3 days is 0.09. Find the mean, of the days per week the men's soccer team plays soccer.
Slide 3: χ P(x) X P(x) 0 0.38 (0)(0.38) = 0 1 0.27 (1)(0.27) = 0.27 2 0.15 (2)(0.15) = 0.3 3 0.09 (3)(0.09) = 0.21 μ = ∑ x P(x) = 0 + 0.27 + 0.3 + 0.21 = 0.78 The probability distribution table was prepared as follows:
Standard Deviation of a Discrete Random Variable: Standard Deviation of a Discrete Random Variable σ = √ ∑ x² P(x) - µ²
Slide 5: χ P(x) X P(x) X² P(x) 0 0.38 (0)(0.38) = 0 0²(0.38) = 0 1 0.27 (1)(0.27) = 0.27 1²(0.27) =0.27 2 0.15 (2)(0.15) = 0.30 2²(0.15) =0.60 3 0.09 (3)(0.09) = 0.21 3²(0.09) = 0.81 σ = ∑ x² P(x) - µ² = (0 + 0.27 + 0.60 + 0.81 ) – 0.78² = 1.68 – 0.6084 = 1.0716
Binomial Probability Distribution: Binomial Probability Distribution Has only 2 possible outcomes Trials are independent Consists of n repeated trials