It is given that . Then,
The joint PDF is
The marginal PDF is
It can be seen that .
Now,
The posterior PDF ,
Let X be a continuous random variable with the following PDF 6x(1 – x) if 0...
PROBLEM 4 Let X be a continuous random variable with the following PDF 6x(1 - 1) if 0 <r<1 fx(x) = o.w. Suppose that we know Y X = ~ Geometric(2). Find the posterior density of X given Y = 2, i.e., fxy (2/2).
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI <x3) Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI
Let X and Y be two jointly continuous random variables with joint PDF xy0x, y < 1 fxy (x, y) O.W Find the MAP and ML estimates of X given Y = y
8. Let X and Y be a random variable with joint continuous pdf: f(x,y)- 0< y <1 0, otherwise a. b. c. Find the marginal PDF of X and Y Find the E(X) and Var(X) Find the P(X> Y)
4. (20%) Let X be a continuous random variable with the following PDF Sce-4x 0<x fx(x) = to else where c is a positive constant. (a) (5%) Find c. (b) (5%) Find the CDF of X, Fx(x). (c) (5%) Find Prob{2<x<5} (d)(5%) Find E[X], and Var(X).
Show all work! Thank you! 0<x<2, 0<y<1 23. The joint pdf of X and Y is fx.y(x, y)= (region below). 3 0 otherwise a) Determine f(y) b) Determine fx, (x) c) Determine E[Yx] d) Determine E[X|y] 0 1 2 24. Suppose that the joint probability density function of the jointly continuous random variables X and Y is x on the given region fxy(x,y)= 11 10 otherwise Determine fyly) 1 _$6x 0<x< y1 25. Let X and Y be continuous random...
2. Let X be a continuous random variable with pdf f(x) = { cr", [w] <1, f() = 0. Otherwise, where the parameter c is constant (with respect to x). (a) Find the constant c. (b) Compute the cumulative distribution function F(2) of X. (c) Use F(2) (from b) to determine P(X > 1/2). (d) Find E(X) and V(X).
3. (10 points) Let X be a continuous random variable with CDF for x < -1 Fx(x) = { } (x3 +1) for -1<x<1 for x > 1 and let Y = X5 a. (4 points) Find the CDF of Y. b. (3 points) Find the PDF of Y. c. (3 points) Find E[Y]
1. Let X and Y be two jointly continuous random variables with joint CDF otherwsie a. Find the joint pdf fxy(x, y), marginal pdf (fx(x) and fy()) and cdf (Fx(x) and Fy)) b. Find the conditional pdf fxiy Cr ly c. Find the probability P(X < Y = y) d. Are X and Y independent?
Let X and Y be continuous random variables with joint pdf f(x,y) =fX (c(X + Y), 0 < y < x <1 otBerwise a. Find c. b. Find the joint pdf of S = Y and T = XY. c. Find the marginal pdf of T. 、