Make the change of variables y = √2x and then relate the resulting expression to the normal distribution.
Answer to relevant QuestionsCompute the hazard rate function of a gamma random variable with parameters (α, λ) and show it is increasing when α ≥ 1 and decreasing when α ≤ 1. Prove Corollary 2.1. Suppose that n points are independently chosen at random on the circumference of a circle, and we want the probability that they all lie in some semicircle. That is, we want the probability that there is a line passing ...Consider independent trials, each of which results in outcome i, i = 0, 1, . . . , k, with probability pi, Let N denote the number of trials needed to obtain an outcome that is not equal to 0, and let X be that outcome. (a) ...The monthly worldwide average number of airplane crashes of commercial airlines is 2.2. What is the probability that there will be (a) More than 2 such accidents in the next month? (b) More than 4 such accidents in the next ...
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