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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 f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; isLet X be a continuous random variable with PDF f(x) = ²/(2-x) for-1 ≤x≤c and f(x) = 0 otherwise. (a) Explaining your work, find the value of the constant c. (b) What is P(X > 1)? (c) Calculate the expectation of X. (d) Calculate the variance of X.
- The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−34. Calculate Var(X+Y) with a full explanationLet X1, X2, and X3 be independent random variables from (-1, 1). Find the probability density function and the expected value of the random variable [X(1) + X(2)]/2.Suppose X and Y are two random variables with covariance Cov(X, Y) = 3 and Var(X) = 16. Find the correlation coefficient between X and Y.
- Develop a random variate generator for a random variable X with the pdf if 0If the random variable X and Y have the joint probability distribution f(x, y) = x+y, 02. Let X be a random variable with density function ) = √(2x² - + f(x) = Find the expected value of g(x) = 2X+1. 8x2 +5x + 6), 1 < x < 2, 0, elsewhereLet X be a continuous random variable with PDF 2x fx\=) = { otherwise Find the expected value of X.The probability function of the random variable X is defined as f(x)=cx²(1-x)² for 0<x<1, otherwise f(x)= 0. Calculate the constant c , the expected value and the variance.Let X and Y be continuous random variables with joint distribution function, F (x,y). Let g (X,Y) and h (X,Y) be functions of X and Y. PROVE Var(a + X) = Var (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