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- Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.Let X and Y continuous random variable with joint pdf fx,y) = 24xy, for 0Let X be a continuous random variable with probability density function fx (x) = 1 (1+x²) , for – 2Let X and Y be jointly continuous random variables with joint PDF cx +1, 2,y> 0, x+ y<1 0, fx,x (x, y) = otherwise. Then the constant c= And the probability that P(Y < 2X²) = ;: Here a = and b =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 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.The 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.Let X1 and X2 be two continuous random variableshaving the joint probability density f(x1, x2) = 4x1x2 for 0 < x1 < 1, 0 < x2 < 10 elsewhereFind the joint probability density of Y1 = X21 and Y2 = X1X2.2. Let X be a continuous random variable with probability density function (pdf) 3x�� 0The random variable X has probability density function 3, 1< a < 2 f(x) = otherwise. Calculate Var(4X +7).Let X be a random variable with pdf: f(x)= k(10 - 2x) for x being [0,5] a.) Find k b.) Find E(X) c.) Find Var(X) d.) Find E(3 *squareroot(X))Let X be a continuous random variable with PDF (2e*,0 /3).SEE 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,