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- Let the joint Probability Density Function of X and Y be: 2*e(x+y) for -infinity<x<y<1. Find the Cov(X, Y) and find the Marginal Probability Density Functions of X and YFind a value of k that will make f a probability density function on the indicated interval. ƒ(x) = kx; [1, 5]Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) = kx; [1, 5]
- The life (in years) of a laptop battery has a probability density function defined by P(x)=12e−x/2P(x)=12e-x/2for x in [0,∞)[0,∞). Find the probability that a randomly selected laptop battery will last between 3 and 8 years?Let X and Y be two continuous random variables with joint probability density function f(x,y) = 2xy for 0 < x < y < 1. Find the covariance between X and Y.Let X and Y be two continuous random variables with joint probability density function f(x,y) = k(x + y) for 0 < x < 1, 0 < y < 1 and 0 otherwise, where k is a constant. Find the marginal probability density functions of X and Y.
- Verify that p(x) = 3x - 4 is a probability density function on [1, oo)and calculate its mean value.Let X be a continuous random variable with density functionf(x) = 3x^-4, x ≥ 1. Compute E(X ) and Var(X ).Suppose that X, Y are jointly continuous with joint probability density function f( x, y){ xe^-x(1+y), ifx >0 and y >00, otherwise. (a) Find the marginal density functions of X and Y. (b) Calculate the expectation E[XY]. (c) Calculate the expectation EIX/(1+ Y )1. (e) Determine if the random variables X and Y in this exercise are independent.
- Suppose the random variables X and Y have joint probability density function f(x,y) given by: (image)Find: P(X < Y) = fX|Y=y (x)Suppose that X ~ Unif[0, 1] and let Y = e^X. (a) Find the cumulative distribution function of Y .(b) Find the probability density function of Y .Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) = kx2; [-1, 2]
