If X is a continuous random variable with X ∼ Uniform([0, 2]), what is E[X^3]?
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If X is a continuous random variable with X ∼ Uniform([0, 2]), what is E[X^3]?
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- Let X be a continuous random variable with PDF (2e*,0 /3).Suppose that X and Y are continuous random variables with joint pdf f (x, y) = e-**) 0Let X be a continuous random variable whose moment generating function is 4x(t) = (5) ³. Find Var (X)Let X be a random variable with pdf f(x) = kx*,-1Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.Suppose we have the quadratic function f(x)=A(x^2)+C where the random variables A and C have densities fA(x)=(x/2) for 0≤x≤2, and fC(x)=3(x^2) for 0≤x≤1. Assume A and C are independent. Find the probability that f(x) has real roots.Let X1, X2, X3 be independent Exp()-distributed random vairables. Determine the pdf of X(1)X(3)Find the mean of random variable of X, if X is random variable with pdf f(x) = c(1-x²), -1Let X1 and X2 be IID exponential with parameter > 0. Determine the distribution ofY = X1=(X1 + X2).Suppose X has PDF fX (x) = 4x(1 − x^2) for 0 < x < 1 (0 everywhere else). Find all mediansand modes for X.(a) Find all medians of X.(b) Find all modes of X.Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample?a) You throw two fair dice labeled 1, . . . , 6 independently of each other and let X be the minimum of the two results. Calculate E[X2]. (b) Suppose that X has pdf given by f(x) = 3x^(−4) if x > 1 and by f(x) = 0 if x <= 1. Calculate the median of X.SEE MORE QUESTIONSRecommended 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