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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.Suppose X is a random variable with the cdf Fy(x) = 1-(1+x²) x>0, c>0, Y>0 Derive the pdf of the inverse of X, Y=1/x²Find the mean of random variable of X, if X is random variable with pdf f(x) = c(1-x²), -1Let X1, X2,... , Xn be independent Exp(A) random variables. Let Y = X(1)min{X1, X2, ... , Xn}. Show that Y follows Exp(nA) dis- tribution. Hint: Find the pdf of YLet X1, X2, X3 be independent Exp()-distributed random vairables. Determine the pdf of X(1)X(3)Let X be a continuous random variable with PDF (2e*,0 /3).3. Let X and Y be continuous random variables with joint PDF (3x 0s ysxs1 f(x, y) = {* otherwise Determine the correlation of variables X and Y.Let X be a continuous random variable whose moment generating function is 4x(t) = (5) ³. Find Var (X)Let Y be a continuous random variable where the pdf of Y is f(y) = 30y* (1 – y), 0< y < 1, and 0 elsewhere. .Find variance of Y 1/25 O 5/196 1/20 O 1/48 2/63 O3. Suppose that X is a continuous random variable with pdf 3x², 0X is a continuous random variable. Note that X = max (0, X) – max (0, -X) show that E (X)= P (X > t) dt – | E P(X < t) dtLet X and Y be two continuous random variables with joint probability density [3x function given by: f(x,y)= 0SEE MORE QUESTIONSRecommended textbooks for youAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage