Let X and Y be continuous random variables with a joint probability density function (pdf) of the form f(x,y) = {k(x+y), 0≤x≤ysı elsewhere Find:
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- Let X and Y be two continuous random variables with joint probability density function f(x,y) = 2xy for 0 < x < y < 1. Find the covariance between X and Y.Let X,Y be two random variables with joint probability density function f(x, y) =0< XLet X be a random variable with density function - 1< x < 2, fn) = fx*/3, f(x) = 0, elsewhere. Find the expected value and the covariance of g(X) = 4X + 3.Let X be a (continuous) uniform random variable on the interval [0,1] and Y be an exponential random variable with parameter lambda. Let X and Y be independent. What is the PDF of Z = X + Y.Let X be a continuous random variable with probability density function fx (x) = 1 (1+x²) , for – 2The probability density of the random variable Z isgiven by f(z) = kze−z2for z > 00 for z F 0Find k and draw the graph of this probability density.The function f(x) is the probability density function, that describes the random variable travel time X. f(x) = {xe®, x>0 0, X ≤0 a.) What is the probability that the travel time is less than 2.5 hours? b.) What is the probability that the travel time is between 1 to 2.5 hours? c.) Find the mean and variance of the given probability density functionThe random variable X has probability density function 3, 1< a < 2 f(x) = otherwise. Calculate Var(4X +7).Let X and Y be two random variables that are independent and have the same probability density function. If U = max (X, Y) V = min (X, Y), find the distribution function of the U random variable using the distribution function technique.The life lengths of two transistors in an electronic circuit is a random vector (X; Y) where X is the life length of transistor 1 and Y is the life length of transistor 2. The joint probability density function of (X; Y) is given by x 2 0, y 2 0 fx.,fx.v) = 20 else Then the probability that the first transistor burned during half hour given that the second one lasts at least half hour equals Select one: a. 0.606 b. 0.3935 C. 0.6318 d. 0.3669 e. 0.7772The function f(x) is the probability density function, that describes the random variable travel time X. f(x) = {xe3,_x>0 0, X ≤ 0 a.) What is the probability that the travel time is less than 2.5 hours? b.) What is the probability that the travel time is between 1 to 2.5 hours?Let X and Y continuous random variable with joint pdf fx,y) = 24xy, for 0SEE MORE QUESTIONSRecommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,