QUESTION 1

Let X be a random variable indicating the water capacity of a dam on a specific date, (varying from 0 indicating the dam is empty to a 1 indicating the dam is full). Assume the water capacity, X, is modelled by df, F: F(x) = x³ . If 7 of the major dams in the Western Cape are observed on this specific date (assume independence), what is the probability that the fullest dam (of the 7) has a capacity more than 0.90?

QUESTION 2

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Question 2 Assume a random variable X be Pareto()-distributed, with E[X] = 20/(0-1) and pdf: f (x ) = 10+1 : x22 and F(x) =1- , x2 2. 0, elsewhere n Let U = min(X).....X,) and let o = _ 0. The distribution of U: i = 1 Select one or more: beta(n,g) O Pareto (ne) O Pareto(0) O Pareto (@) Pareto (n + 0) Question 3 Assume a random variable X is Pareto(@)-distributed, with E[X] = 20/(0-1) and pdf: 020 f ( x ) = 8+1 x22 0, elsewhere Let U = min(X],...,X5). If 0 = 2, then E[U] is equal to