If X is a random variable having the standard nor–mal distribution and Y = X2, show that cov(X, Y) = 0 even though X and Y are evidently not independent.
Answer to relevant QuestionsUse the Maclaurin’s series expansion of the moment-generating function of the standard normal distribution to show that (a) µr = 0 when r is odd; (b) µr = r! 2r / 2r/2(r/2)! when r is even. Show that when α → ∞ and β remains constant, the moment-generating function of a standardized gamma random variable approaches the moment-generating function of the standard normal distribution. In certain experiments, the error made in determining the density of a substance is a random variable having a uniform density with α = – 0.015 and β = 0.015. Find the probabilities that such an error will (a) Be ...If the annual proportion of erroneous income tax returns filed with the IRS can be looked upon as a random variable having a beta distribution with α = 2 and β = 9, what is the probability that in any given year there will ...If zα is defined by Find its values for (a) α = 0.05; (b) α = 0.025; (c) α = 0.01; (d) α = 0.005.
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