i need help with both! QUESUU 41 POINTS Let Xhave the probability density function f(x) =...
[4+3+3 Points] 9. For the following probability density function, f(x) -k for 0 <x < 0.5 f(x) - 3x2 for 0.5 < x < 1 f(x) -0 otherwise What is the value of k? Find the median value of x Find the probability that X<0.75 a. b.
5. Let X and Y have joint probability density function of the form Skxy if 0 < x +y < 1, x > 0 and y > 0, f(x,y)(, y) = { 0 otherwise. (a) What is the value of k? (b) Giving your reasons, state whether X and Y are dependent or independent. (c) Find the marginal probability density functions of X and Y. (d) Calculate E(X) and E(Y). (e) Calculate Cov(X,Y). (f) Find the conditional probability density function...
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.
Homework help with 7.63 please 7.63 Let the random variable X have probability density function f(x)= -π/2 < x <π/2. Find the probability density function of Y sin X by the (a) cumulative distribution function technique, (b) transformation technique. dx1 Hint: The derivative oh-arcsiny is
2.6.9 Let X have density function fx(x) = x/4 for 0 < x < 2, otherwise fx(x)=0. (a) Let Y = X. Compute the density function fy(y) for Y. (b) Let Z = X. Compute the density function fz(z) for Z.
b. Let X be a continuous random variable with probability density function f(x) = kx2 if – 1 < x < 2 ) otherwise Find k, and then find P(|X| > 1/2).
Let X1, ... , Xn be a sample from the probability density function f(x0), where 0 € {0,1}. If 0 = 0, then f(20) = ſi if 0<x<1, 10 otherwise, while if @= 1, then fale) - 27if 0<x< 1, 10 otherwise. Find the MLE of 0.
6. Let X be a continuous random variable whose probability density function is: 0, x <0, x20.5 Find the median un the mode. 7. Let X be a continuous random variable whose cumulative distribution function is: F(x) = 0.1x, ja 0S$s10, Find 1) the densitv function of random variable U-12-X. 0, ja x<0, I, ja x>10.
Let f(x,y) = exp(-x) be a probability density function over the plane. Find the probabilities: Parta)P( X2 + y2 <a), a > 0, Part b)P(x2 + y2 <a), a > 0.
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)