Show that the probability density function of a negative binomial random variable equals the probability density function of a geometric random variable when r _ 1. Show that the formulas for the mean and variance of a negative binomial random variable equal the corresponding results for geometric random variable when r _ 1.
Answer to relevant QuestionsSuppose that X is a negative binomial random variable with p _ 0.2 and r _ 4. Determine the following: (a) E(X1) (b) P(X =20) (c) P(X =19) (d) P(X =21) (e) The most likely value for XSuppose X has a hypergeometric distribution with N = 100, n = 4, and K = 20. Determine the following: (a) P(X = 1) (b) P(X =6) (c) P(X =4) (d) Determine the mean and variance of X.Magnetic tape is slit into half-inch widths that are wound into cartridges. A slitter assembly contains 48 blades. Five blades are selected at random and evaluated each day for sharpness. If any dull blade is found, the ...The number of flaws in bolts of cloth in textile manufacturing is assumed to be Poisson distributed with a mean flaw per square meter. (c) What is the probability that there are no flaws in 20 square meters of cloth? (d) ...Continuation of Exercise 3-109. (a) What is the probability that you must call six times in order for two of your calls to be answered in less than 30 seconds? (b) What is the mean number of calls to obtain two answers in ...
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