function Ckek osrs4 be a density 4. Let f(x)=3 otherwise Find: i) k = 24] P(-2<x<2)
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).
Q1. Let X and Y have joint density 0, otherwise. a. Find the marginal densities of X and Y b. Find P(0.2 < Y < 0.31X = 0.8).
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise. (a) Find c (b) Find the distribution function Fx) (c) Compute P(l <X<3)
Consider the following pdf: ; 0<x<1 f(x)-2k ; l<x<2 0 otherwise (i)Determine the value of k. (ii) Find P(X 0.3) (iii) Find (0.1 〈 X 1.5).
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.
If X and Y have a joint probability density function specified by 2-(+2y) find P(X <Y).
The random variable X has probability density function k(x25x-4) 1<x<4 otherwise -{ f(x) 1. Show thatk. (5pts) Find 2. Е (X), (5pts) 3. the mode of X, (5pts) 4. the cumulative distribution function F(X) for all x. (5pts) 5. Evaluate P(X < 2.5). (5pts) 6. Deduce the value of the median and comment on the shape of the distribution (10pts)
The density function of X is given by + br if 0 r < 1 f(x) = 0 1 otherwise If E(X) = 3, find a and b. (Hint: Both values are integer.) a = b =
Problem 29.1 Let X have the density function given by 0.2 -1<r<0 f(x) = 0.2 + cx 0 〈 x < 1 otherwise. (a) Find the value of c.
2) Suppose that X has density function f(a)- 0, elsewhere Find P(X < .3|X .7).