If p(x) = = var(X)= sd(X)= x 15 ‚ for x = 1, 2, 3, 4, 5, is the probability mass function of a random variable X, then E(X)=||
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- For the continuous probability function f (x) = Kx² e* when x20 fint i) k i) mean iii) varianceLet X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.A random variable X has the probability density function as f(x) = Ax(9-X2) 0 ≤ x ≤ 3 = 0 otherwise Find the value of A, the mean and the standard deviation of X.
- Let joint Probability distribution function of random variables X and Y be if (x, y) = (1, 1) 1/3 |1/3 if (x, y) = (0, 0) (1/3 if (x, y) = (2, 0) P(x, y)={ otherwise . Are X and Y independent?If X is a random variable with probability density function 32 f(x) = A* for x = 0, 1, 2, 3, 4 and 5, the var(X)Let 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.
- For the continuous probability function f(x) = Kx² ex when x ≥ 0 find i) k ii) mean iii) variance =(A=X) qLet f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; isLet p(x) = cx^2 for the integers 1, 2, and 3 and 0 otherwise. What value must c be in order for p(x) to be a legitimate probability mass function?
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