Show that if α > 1 and β > 1, the beta density has a relative maximum at
Answer to relevant QuestionsVerify the expression given for µ'2 in the proof of Theorem 6.5. Show that the normal distribution has (a) A relative maximum at x = µ; (b) Inflection points at x = µ – σ and x = µ + σ. Show that if a random variable has a uniform density with the parameters α and β, the rth moment about the mean equals (a) 0 when r is odd; (b) 1 / r + 1 (β – α / 2)r when r is even. If X and Y have a bivariate normal distribution, it can be shown that their joint moment– generating function (see Exercise 4.48 on page 139) is given by Verify that (a) The first partial derivative of this function with ...The number of planes arriving per day at a small private airport is a random variable having a Poisson distribution with λ = 28.8. What is the probability that the time between two such arrivals is at least 1 hour?
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