Question: Let T have a t distribution with r degrees of
Let T have a t distribution with r degrees of freedom. Show that E(T) = 0 provided that r ≥ 2, and Var(T) = r/(r − 2) provided that r ≥ 3, by first finding E(Z), E(1/√U), E(Z2), and E(1/U).
Answer to relevant QuestionsLet n = 9 in the T statistic defined in Equation 5.5-2. (a) Find t0.025 so that P(−t0.025 ≤ T ≤ t0.025) = 0.95. (b) Solve the inequality [−t0.025 ≤ T ≤ t0.025] so that μ is in the middle. Let X and Y equal the respective numbers of hours a randomly selected child watches movies or cartoons on TV during a certain month. From experience, it is known that E(X) = 30, E(Y) = 50, Var(X) = 52, Var(Y) = 64, and ...In the casino game roulette, the probability of winning with a bet on red is p = 18/38. Let Y equal the number of winning bets out of 1000 independent bets that are placed. Find P(Y > 500), approximately. A candy maker produces mints that have a label weight of 20.4 grams. Assume that the distribution of the weights of these mints is N(21.37, 0.16). (a) Let denote the weight of a single mint selected at random from the ...A small part for an automobile rearview mirror was produced on two different punch presses. In order to describe the distribution of the weights of those parts, a random sample was selected, and each piece was weighed in ...
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