# Question: Show that the moment generating function of the geometric distribution is

Show that the moment-generating function of the geometric distribution is given by

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Use the moment–generating function derived in Exercise 5.20 to show that for the geometric distribution, µ = 1/θ and σ2 = 1 – θ / θ2. When calculating all the values of a hypergeometric distribution, the work can often be simplified by first calculating h(0; n, N, M) and then using the recursion formula Verify this formula and use it to calculate the ...Use repeated integration by parts to show that This result is important because values of the distribution function of a Poisson random variable may thus be obtained by referring to a table of incomplete gamma functions. An automobile safety engineer claims that 1 in 10 automobile accidents is due to driver fatigue. Using the formula for the binomial distribution and rounding to four decimals, what is the probability that at least 3 of 5 ...(a) To reduce the standard deviation of the binomial distribution by half, what change must be made in the number of trials? (b) If n is multiplied by the factor k in the binomial distribution having the parameters n and ...Post your question