Show that f(x, y) is a joint pdf and the two marginal pdfs are each normal. Note that X and Y can each be normal, but their joint pdf is not bivariate normal.
Answer to relevant QuestionsShow that the expression in the exponent of Equation 4.5-2 is equal to the function q(x, y) given in the text. Let f(x) = 1/[π(1 + x2)], −∞ < x < ∞, be the pdf of the Cauchy random variable X. Show that E(X) does not exist. Let W1, W2 be independent, each with a Cauchy distribution. In this exercise we find the pdf of the sample mean, (W1 + W2)/2. (a) Show that the pdf of X1 = (1/2)W1 is (b) Let Y1 = X1 + X2 = W and Y2 = X1, where X2 = (1/2)W2. ...Let X1, X2, X3 be a random sample of size n = 3 from the exponential distribution with pdf f(x) = e−x, 0 < x < ∞. Find P(1 < min Xi) = P(1 < X1, 1 < X2, 1 < X3) Let X equal the outcome when a fair four-sided die that has its faces numbered 0, 1, 2, and 3 is rolled. Let Y equal the outcome when a fair four-sided die that has its faces numbered 0, 4, 8, and 12 is rolled. (a) Define ...
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