ACC Exam II - Chapte r5 5.2 5.3 Discrete Probability Distributions For each random variable x the probability distribution is denoted by f(x Required

# ACC Exam II - Chapte r5 5.2 5.3 Discrete Probability...

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Chapte r 5 5.2 Discrete Probability Distributions For each random variable x, the probability distribution is denoted by f(x) Required conditions: f(x) > 0 and E f(x) = 1 Example: x f(x) 0 0.18 1 0.39 2 0.24 3 0.14 4 0.04 5 0.01 5.3 Expected value, variance and standard deviation Expected Value: E (x) = u = E xf(x) Example: E(x) = 1.50 Variance:  E (x - u) 2 f(x) Example: x f(x) Sq Dev from Mean 0 0.18 2.25 1 0.39 0.25 2 0.24 0.25 3 0.14 2.25 4 0.04 6.25 5 0.01 12.25  1.25 Std Deviation: Square Root ( Example:  1.118 5.4 Binomials: n = number of trials p = probability of success x = number of successes TRUE = argument of any specific value of x FALSE = argument of the cumulative probability of x For values of x, where x f(x = y) = BINOMDIST(y,n,p,FALSE) f(x > y) = 1-BINOMDIST(y,n,p,TRUE) f(x < y) = BINOMDIST((y-1),n,p,TRUE) f(x > y) = 1-BINOMDIST((y-1),n,p,TRUE) f(x < y) = BINOMDIST(y,n,p,TRUE) Expected Value: E (x) = u = np Variance:  np(1 - p) Std Deviation: Square Root (