Show that if the limiting conditions n → ∞, θ → 0, while n. remains constant, are applied to the moment–generating function of the binomial distribution, we get the moment-generating function of the Poisson distribution.
Answer to relevant QuestionsUse Theorem 5.9 to show that for the Poisson distribution α3 = 1/√λ, where α3 is the measure of skewness defined in Exercise 4.26 on page 129. Theorem 5.9 The moment-generating function of the Poisson distribution is ...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 ...In planning the operation of a new school, one school board member claims that four out of five newly hired teachers will stay with the school for more than a year, while another school board member claims that it would be ...If the probability is 0.75 that a person will believe a rumor about the transgressions of a certain politician, find the probabilities that (a) The eighth person to hear the rumor will be the fifth to believe it; (b) The ...What is the probability that an IRS auditor will catch only 2 income tax returns with illegitimate deductions if she randomly selects 5 returns from among 15 returns, of which 9 contain illegitimate deductions?
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