5. Suppose that the probability distribution function (p.d.f.) of a random variable X is as follows:...
1. Suppose that the p.d.f. of a random variable X is as follows: for 0<x<2, for 0 〈 x 〈 2. r for 0<< f(x) = 0 otherwise. Let Y - X (2 - X). First determine the c.d.f. of Y, then find its p.d.f. (Hint: when computing c.d.f., plotting the function Y- X(2 - X) which may help. )
A probability distribution function for a random variable X has the form Fx(x) = A{1 - exp[-(x - 1)]}, 1<x< 10, -00<x<1 (a) For what value of A is this a valid probability distribution function? (b) Find the probability density function and sketch it. (c) Use the density function to find the probability that the random variable is in the range 2 < X <3. Check your answer using the distribution function. (d) Find the probability that the random variable...
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)
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.
121 Q1. If x is continuous variable and follows probability density function x/7; 2<x<4 f(x) = then find the value of P(2<x<3) ? 0; otherwise
Suppose that X is a continuous random variable with probability distribution Suppose that X is a continuous random variable with probability distribution O<x<6 18 (a) Find the probability distribution of the random variable Y-10X 3. fr o) 2 Edit for Sy s (b) Find the expected value of Y
help solve Question 9. Given the c.d.f of a continuous random variable X as: 0 if x < 0 Fx(x)= x3 if 0 sxs1 1 otherwise Write down the p.d.f of X.
(1) Suppose that X is a continuous random variable with probability density function 0<x< 1 f() = (3-X)/4 i<< <3 10 otherwise (a) Compute the mean and variance of X. (b) Compute P(X <3/2). (c) Find the first quartile (25th percentile) for the distribution.
[Q#2] (7pts) Suppose a discrete random variable Y has a Geometric probability distribution with probability of success p (>0). Its p.d.f. p(y) is defined as P(Y = y) = p(y) = p (1-p)y-1 for y = 1,2,3, ... Verify that the sum of probabilities when the values of random variable Y are even integers only is 1-p. That is to find p(2) + p(4) +p(6) +.. 2 – p
Suppose that X and Y are jointly continuous random variables with joint probability density function f(x,y) = {12rºy, 1 0, 0<x<a, 0<y<1 otherwise i) Determine the constant a ii) Find P(0<x<0.5, O Y<0.25) HE) Find the marginal PDFs fex) and y) iv) Find the expected value of X and Y. Le. E(X) and E(Y) v) Are X and Y independent? Justify your answer.