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.
Answer to relevant QuestionsTo prove Theorem 6.10, show that if X and Y have a bivariate normal distribution, then (a) Their independence implies that ρ = 0; (b) ρ = 0 implies that they are independent. Theorem 6.10 If two random variables have a ...Use the results of Exercise 6.4 to find α3 and α4 for the uniform density with the parameters α and β. The number of bad checks that a bank receives during a 5-hour business day is a Poisson random variable with λ = 2. What is the probability that it will not receive a bad check on any one day during the first 2 hours of ...If Z is a random variable having the standard nor–mal distribution, find the respective values z1, z2, z3, and z4 such that (a) P(0 < Z < z1) = 0.4306; (b) P(Z ≥ z2) = 0.7704; (c) P(Z > z3) = 0.2912; (d) P(–z4 ≤ Z ...A random variable has a normal distribution with σ = 10. If the probability that the random variable will take on a value less than 82.5 is 0.8212, what is the probability that it will take on a value greater than 58.3?
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