Determine K and the distribution function.
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- A continuous random Variable X has probability Density function defined by f(x) = 5-5x; 0Let x be a continuous random variable with the density function: f(x) = 3e-3x when x>0 and 0 else Find the variance of the random variable x.Suppose the random variable Y has an exponential distribution with mean 2. Use the method of transformations to find the density function of U=(1/5)Y+3
- Suppose that Y1, . . . , Yn is a random sample from a population whose density function isIf two random variables X1 and X2 have the joint density function given by f (x1, x2) = x1x2, 0 < x1 < 1, 0 < x2 < 2 0, otherwise Find the probability that (a) Both random variables will take on values less than 1 (b) The sum of the values taken on by the two random variables will be less than 1.Consider two random variables X and Y whose joint probability density function is given byf_X,Y (x, y) = c if x + y ≤ 1, x ≤ 1, and y ≤ 1,0 otherwise What is the value of c?