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- Let the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3, Find the variance of X.What is the variance of a continuous random variable X whose probability density isFind the mean of random variable of X, if X is random variable with pdf f(x) = c(1-x²), -1The probability function of a continuous random variable, X, is given by the equation: fx(x) = 0.0064x(25-x²) for 0 < X < 5 Draw plots of both the pdf and the cdf of X.The pdf of random variable X is given as ƒx(x) = Find the i) Mean ii) Mean of the square [0.3507√x 0Find the characteristic function of X² when X has the N(u, o²) distribution.(4) Let X be a discrete random variable with domain D. Prove that Var(X) = E(X?) – E(X).Consider the random variable X with PDF (known as Cauchy distri- bution) f(x) = 7 - 00Suppose V Geom(p) with p = 0.66 and that W 2V. Find P(W > 8), giving your answer correct to two decimal places.The time to wait between each phonecall a person recives is random given f(t) = 3e-3t for t>=0. Let T1 and T2 be two independent waiting times for this distribution. Find expected time between each call and variance. (E(T) and V(T)) Find the probability for both T1 and T2 to be greater than one.Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; isRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON