Suppose X~U[-1,1], calculate distribution function and probability density function of Y=X^2. Plz help
Suppose X~U[-1,1], calculate distribution function and probability density function of Y=X^2. Plz help
7.4 Let X ~U(_ 1,1 ) and Y =X2. What are the density, the distribution function, the mean, and the variance of Y What is Pr[Y s0.5]? a. b.
7.4 Let X ~ U(-1,1) and Y = x2. a. What are the density, the distribution function, the mean, and the variance of Y: b. What is Pr[Y < 0.5]? 7.5 Let X – U(0,1), and let Y = eax for some a > 0. What are the density, the distribution function, the mean, and the variance of Y?
2. Suppose that the random variables X and Y have joint probability density function given by f(x, y) = 18(x - x?)y?, 0SX S1, OS y si. Let U = XY. Find the density function of U.
2. Suppose that (X,Y) has the following joint probability density function: f(x,y) = C if -1 <r< 1 and -1 <y<1, and 0 otherwise. Here is a constant. (a) Determine the value of C. (b) Are X and Y independent? (Explain why or why not.) (c) Calculate the probability that 2X - Y > 0 (d) Calculate the probability that |X+Y| < 2 3. Suppose that X1 and X2 are independent and each is standard uniform on (0,1]. Let Y...
If X ~U(-2; 4), find the probability density function of the random variable: a) Y = 2X + 3. b) Y = 1/(X+2)4 c) Y = X2u(X), where u(x) is the unit step function. Hint: first sketch g(x) = x2u(x)
Suppose X and Y are jointly continuous random variables with joint density function Let U = 2X − Y and V = 2X + Y (i). What is the joint density function of U and V ? (ii). Calculate Var(U |V ). 1. Suppose X and Y are jointly continuous random variables with join density function Lei otherwise Let U = 2X-Y and V = 2X + y (i). What is the joint density function of U and V? (ii)....
asap plz The joint probability density function of random variables X and Y is given by, otherwise a. Find k b. Find the best (non-linear) minimum mean squared error (MMSE) estimator for Y given X-r. 20]
Suppose that U~Unif[0,1]. Let . Find the probability density function of Y.
A distribution is given as X~ U (0,6). (a) What is the probability density function? (b) What is the mean of the distribution? (c) What is the standard deviation of the distribution? (d) Find P (x>4)
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)