6. Suppose that X has the uniform distribution on the interval [a, b]. Determine the m.g.f. of X.
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- The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the conditional probability of the event E, getting a six, given that the event F, getting an even number, has occurred is P(EF)=___________.Suppose that X has a hypergeometric distribution with N = 2,000, K = 800, and n = 200. Find the probability P (X ≤ 70) based on the corresponding hypergeometric distribution and approximate normal distribution. Is the normal approximation reasonable?If X1, X2, ... , Xk have the multinomial distribution of Definition 8, show that the mean of the marginal distribu-tion of Xi is nθi for i = 1, 2, ... , k.
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- Find the z value so that 7.49% of the area under the distribution curve lies to the right of it.Suppose the variables Q and W are skewed distributions defined over a limited set of values. What is the probability that Q takes on a value between ½ and 1? What is E(Q)?A weather forecaster predicts that the may rainfall in a local area will be between three and six inches but has no ides where within the interval the amount will be. Let x be the amount of M ay rainfall in the local area, and assume that x is uniformly distributed over the interval three to six inches. What is the probability that May rainfall will be at least four inches? At least five inches?