Let X be a random variable with the probability density function f(x)= x^3/4 for an interval...
3. (10 points) Let X be continuous random variable with probability density function: fx(x) = 7x2 for 1<<2 Compute the expectation and variance of X 4. (10 points) Let X be a discrete random variable uniformly distributed on the integers 1.... , n and Y on the integers 1,...,m. Where 0 < n S m are integers. Assume X and Y are independent. Compute the probability X-Y. Compute E[x-Y.
be a continuous random variable with probability density function 3. Let for 0 r 1 a, for 2 < < 4 0, elsew here 2 7 fx(x) = (a) Find a to make fx(x) an acceptable probability density function. (b) Determine the (cumulative) distribution function F(x) and draw its graph.
2x 0<x<1 Let X be a continuous random variable with probability density function f(x)= To else The cumulative distribution function is F(x). Find EX.
4. Let X and Y have joint probability density function f(x,y) = 139264 oray3 if 0 < x, y < 4 and y> 4-1, otherwise. (a) Set up but do not compute an integral to find E(XY). (b) Let fx() be the marginal probability density function of X. Set up but do not compute an integral to find fx(x) when I <r54. (c) Set up but do not compute an integral to find P(Y > X).
3. Let X be random variable with probability density function x(x)4 for 0 x 1, (Note: fx (x) = 0 outside this domain.) (a) Find E[X] and Var[X] (b) Let Y- X2 +5. Find E[Y] and Var[Y]. (c) Find PX 112 ).
Let X be a continuous random variable with probability density function fX(x)=2x for 0 < x <1. What is the expected value of X.
Suppose the random variable X has probability density function (pdf) - { -1 < x<1 otherwise C fx (x) C0 : where c is a constant. (a) Show that c = 1/7; (b) Graph fx (х); (c) Given that all of the moments exist, why are all the odd moments of X zero? (d) What is the median of the distribution of X? (e) Find E (X2) and hence var X; (f) Let X1, fx (x) What is the limiting...
Let X be a continuous random variable with probability density function fx()o otherwise Find the probability density function of YX2 Let X be a continuous random variable with probability density function fx()o otherwise Find the probability density function of YX2
I . (20%) Random variable X has the probability density function as ; Random variable Y 2X+1 0 otherwise a) Determine A b) Determine the Probability Distribution Function F, (x) c) Determine E(X) and ơx d) Determine the probability density function fy(y) and E(Y)
3.98 Let X be a continuous random variable with probability density function f(x) defined on = {xl-π/2 < x < π/2). Give an expression for VIsinX)