-3x > 0 An exponential distribution is given by f(x) zero, x <0 Find the distribution...
I. Let X be a random sample from an exponential distribution with unknown rate parameter θ and p.d.f (a) Find the probability of X> 2. (b) Find the moment generating function of X, its mean and variance. (c) Show that if X1 and X2 are two independent random variables with exponential distribution with rate parameter θ, then Y = X1 + 2 is a random variable with a gamma distribution and determine its parameters (you can use the moment generating...
Show steps, thanks! 2.5.9. The random variable X has a cumulative distribution function 0, forx<0 F(x) for x > 0. for x > , 1+x2" · Find the probability density function of X.
The velocity of a particle in a gas is a random variable X with probability distribution fx(x) = 27 x2 -3x x >0. The kinetic energy of the particle is Y = {mXSuppose that the mass of the particle is 64 yg. Find the probability distribution of Y. (Do not convert any units.)
(+3) The pdf f(x) of a random variable X is given by 0, ifx<0 Find the cumulative distribution function F(r
Suppose X and Y are independent random variables with Exponential(2) distribution (Section 6.3). We say X ~ Exponential(2) if its pdf is f(x) = -1/2 for x > 0.
1 x Suppose X has an exponential distribution, thus its pdf is given by fx (x) = 5e8,0 5x<0, 2> 0;0 0.w. a. Find E(X) b. Find E(X(X-1) c. Find Var (x)
The velocity of a particle in a gas is a random variable X with probability distribution fx(x) = 27x2e-3x x >0. The kinetic energy of the particle is Y = mx?. Suppose that the mass of the particle is 64 yg. Find the probability distribution of Y. (Do not convert any units.)
9. The distribution function of a random variable X is given by 0, for r<-1, F(x) = { 271 -1<x<1, 1, 2 > 1. Find (a) P(Z < X < }); (b) P(1<x< 2).
4. Let X be a continuous random variable with probability density function: x<1 0, if if| if x>4 f(x) = (x2 + 1), 4 x 24 0 Find the standard deviation of random variable X.
Q2. Assume that X is a continuous and nonnegative random variable with the cumulative distribution function Fx Let b> 0. (a) Find the cumulative distribution function of Y = XI(X < b} (b) Apply the general formula from (a) to exponential distribution with parameter λ > 0.