TRY to generalize it for any finite number of independent exponential random variable S. Let Xk - Exp(?k), k = 1, 2, ., n be independent. Compute probabilitylP (X1 = X2 = = Xn)?
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- For independent random variables X and Y, we have var(X -Y) = var(X)-var(Y ). * true FalseAn ordinary (fair) coin is tossed 3 times. Outcomes are thus triple of “heads” (h) and tails (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is hht, then R (hht)=1. Suppose that the random variable X is defined in terms of R as follows X=6R-2R^2-1. The values of X are given in the table below. A) Calculate the values of the probability distribution function of X, i.e. the function Px. First, fill in the first row with the values X. Then fill in the appropriate probability in the second row.Suppose that f(x)=2/(3^x), x=1,2,3,... is the probability function for a random variable X. Find P(X>3). Use 4 decimal places.
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