Find the moment-generating function of the negative binomial distribution by making use of the fact that if k independent random variables have geometric distributions with the same parameter θ, their sum is a random variable having the negative binomial distribution with the parameters θ and k.
Answer to relevant QuestionsIf n independent random variables have the same gamma distribution with the parameters α and β, find the moment-generating function of their sum and, if possible, identify its distribution. With reference to Exercise 3.93 on page 107, find the probability density of the average mileage of two such tires. Assume independence. With reference to Exercise 3.102 on page 108, find the probability density of the random variable Z = X+ Y / 2 , which is the average of the two proportions of correct answers that a student will get on the two aptitude ...If the number of complaints a dry-cleaning establishment receives per day is a random variable having the Poisson distribution with λ = 3.3, what are the probabilities that it will receive (a) 2 complaints on any given ...If the joint density of X and Y is given by And Z = X + Y / 2 , find the probability density of Z by the distribution function technique.
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