# Question: Use integration by parts to show that

Use integration by parts to show that Γ(α) = (α – 1) ∙ (α – 1) for Γα > 1.

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Suppose that during periods of meditation the reduction of a person’s oxygen consumption is a random variable having a normal distribution with µ= 37.6 cc per minute and s = 4.6 cc per minute. Find the probabilities that ...Suppose that we want to use the normal approximation to the binomial distribution to determine b(1;150,0.05). (a) Based on the rule of thumb on page 192, would we be justified in using the approximation? (b) Make the ...Using the form of the gamma function of Exercise 6.8, we can write And hence Change to polar coordinates to evaluate this double integral, and thus show that (12 ) = v p. In exercise If the probability density of X is given by Where k is an appropriate constant, find the probability density of the random variable Y = 2X / 1+ 2X . Identify the distribution of Y, and thus determine the value of k. If the joint probability distribution of X and Y is given by f(x, y) = (x– y)2 / 7 for x = 1, 2 and y = 1, 2, 3, find (a) The joint distribution of U = X + Y and V = X – Y; (b) The marginal distribution of U.Post your question