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- let X and Y be independent standard normal random variables. Determine the pdf of W = X^2 + Y^2. Find the mean and the variance of U= (1/2)WThe density of a random variable X is f(x) = C/x^2 when x ≥ 10 and 0 otherwise. Find P(X > 20).Let X and Y be two independent continuous random variables with the following probability density functions: f(x) = (1/2)e^(-x/2) for x > 0 g(y) = (1/3)e^(-y/3) for y > 0 What is the probability density function of Z = X + Y?
- 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.A continuous variable Y has a probability density function for which the moment generating function is given by M(t)=e^(2*t+72*t^2). What is the variance of the variable, Var[Y]?Find the expected value and variance of the random variableX whose density function is f(x) = 1/(2(x)^0.5), 1 ≤ x ≤ 4.
- Q3/ consider a random variable X with density function 0.125(4 + 2x) 1< x < 2 f (x) = elsewhere Find the variance for g(X) = 4X +3Find the probability distribution of the random variable y, which represents the number of times writing appears when a balanced coin is tossed three times. Calculate the mean and variance of the random variable y, whose probability mass function is: f (y) = y^2/30 y = 1,2,3Suppose that X is a random variable with density and suppose that ?=e(-4X) Determine ?(?)
- Let X be a continuous random variable with range [1,3] and its probability density function is given by the following function: f(x)=c/(x^3) where c is a constant. (1) Find the value of c . Answer: (2) Find the expected value of X . Answer:2x A random variable X has the density function f(x)= } k- 0, Otherwise. For what value of k the variance of X equal to 2.If a dealer’s profit, in units of $5000, on a new automobile can be looked upon as a random variable X having the density function Find the variance of X.