54. Find a constant C such that |Сху p(x, y) = if 0 < x and 0 < y<1- x otherwise is a joint probability density function. Then calculate: 'a) P(X < };Y < ) (b) Р(X 2 Y)
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- 7. Assume that X and Y have joint probability density function given by (2x + 3y) if 0< x<1 and 06. Let f be a function (2, if 01). (c) Find P(X 0.5).Let f(x) = Ce-x/1+e-2x for all x in (-infinity, infinity). If f is a probability density function for a random variable X on (-infinity, infinity), answer the following: (a) Find the value of constant C. (b) Evaluate the probability P(X<-4). Correct to four decimal places.Suppose that X and X, have joint probability density function x2, if 1< xı < 2 and 1 < r2 < 3 10, fx1.x.("1, 2) = otherwise. What is the joint probability density function fy,y, of Y1 = X1/X2 and Y, = X2?Let X and Y be continuous random variables with joint probability density function f(x, y) = (3/200y if 0 < 5x < y < 10 O otherwise Find Cov(X, Y)сх, f(x)= 0If X has the probability density * 21 f(2): 2 <1 Find P (1 < X < 5). Select one: O a. 0.93 O b. 0.96 O G 0.12 O d. 0.91If X is uniformly distributed over [ -1, 2], find () the cumulative distribution function of Y1 = |X. (1) Find the probability density function of Y =exLet x and y have joint density function * + 2y), for 0 3 Enter the exact answer. (1>}) - 3 1 (b) Find the probability thatx < + y. Enter the exact answer. px +The joint probability density is for X and Y are f(x, y). Give the exact answer. S 2 (x + y) 0 < x < 1, 0 < y < 1, y < x f (x, y)= elsewhere P (x < }, y < })=. Р (х 2, y < )-Suppose a college professor never finishes her lecture before the end of the class period, and always finishes within five minutes after the class period is supposed to end. Let X = time that elapses between the end of the class period and the actual end of the lecture. Suppose the pdf of X is: (image) Find the value of k that makes f(x) a legitimate probability density function, and use that value of k to find the probability that the lecture ends less than 3 minutes after the class period is supposed to end.Let X will be continuous random variable with probability density function as below. f(x) = {4x , (0Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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