The joint probability density function of X and Y is given by Find c and the expected value of X: E(X) = f(x, y) = c(y² – 196x²)e™, - 1/4 У 14 У ≤ x ≤ 11/4, 0 < y < ∞
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- The joint probability density function of X and Y is given byf(x,y) = x+y 0 < x < 1, 0 < y < 1 (d) E(xy) = ? (e) Cov(x,y) = ?Calculate the E(X) when the joint probability density function of X and Y is fxy(X,Y)=c(X+Y) over the range x = 1, ..., 4 and y = 1, ..., 2For the probability density function f(x) = 3x^2 on [0,1], find: V(X)
- Find the value of k that makes the given function a probability density function on the specified interval.f(x) = kx2, 0 ≤ x ≤ 2Suppose that two continuous random variables X and Y have joint probability density function fxy = A( ex+y + e2x+y) , 1 ≤ x ≤ 2 ,0≤ y≤3 0 elsewhere a. P ( 3/2 ≤ X ≤ 2, 1 ≤ Y ≤ 2) b. Are the random variables X and Y independent? c. find the conditional density X given Y = 0Find the value of k that makes the given function a probability density function on the specified interval.f(x) = kx, 1 ≤ x ≤ 3
- Find a value of k that will make f a probability density functionon the indicated interval.ƒ(x) = kx; [0, 3]Suppose that X and Y have a joint probability density function f(x,y)= 1, if0<y<1,y<x<2y; 0, otherwise. (a) Compute P(X + Y less than or equal 1). (b) Find the marginal probability density functions for X and Y , respectively. (c) Are X and Y independent?Q3) The joint probability density function of two discrete random variables X and ¥ is given by p(x, y)=c(2x+3y), where x and can assume all integers such that 0 <
- The PDF of a continuous random variable X is as follows: f(X)= c(4x2 - 2x2) 0<* x <* 2 (*less or equal to) a. For this to be a proper density function, what must be the value of c ?Determine the conditional probability distribution of Y given that X = 1. Where the jointprobability density function is given by f(x,y)=1/64xy for 0 < x < 4 and 0 < y < 4.Find the constant C such that p is a probability density function on the given interval and compute the probaility P(X< 2)
