1. A continuous random variable X has density function given by 0 elsewhere. (a) (8 pts.)...
Q 2. The probability density function of the continuous random variable X is given by Shell, -<< 0. elsewhere. f(x) = {&e*, -40<3<20 (a) Derive the moment generating function of the continuous random variable X. (b) Use the moment generating function in (a) to find the mean and variance of X.
Let X be a continuous random variable with density function: f(x) ={: 0.41x-1, 03x 33 0 sx33 , elsewhere Compute E[X]
A continuous random variable X has the probability density function f(x) = e^(-x), x>0 a) Compute the mean and variance of this random variable. b) Derive the probability density function of the random variable Y = X^3. c) Compute the mean and variance of the random variable Y in part b)
Problem 3. The random variable X has density function f given by 0, elsewhere (a) Assuming that 6 0.8, determine K (b) Find Fx(t), the c.d.f. of X (c) Calculate P(0.4 <X < 0.8)
Suppose that the density function of a continuous random variable is given by f(x)=c(e-2x-e-3x) for non-negative x, and 0 elsewhere a) Determine c b) Compute P(X>1) c) Calculate PX<0.5 X<1.0)
1. Let X be a continuous random variable with the probability density function fx(x) = 0 35x57, zero elsewhere. Let Y be a Uniform (3, 7) random variable. Suppose that X and Y are independent. Find the probability distribution of W = X+Y.
4. Let X be a continuous random variable with probability density 1 0< x<3 -x + k =6 f(x) elsewhere 0, Evaluate k. a. b. Find P(1 < X< 2). c. Find E(X) d. Find e. Find ox. 4. Let X be a continuous random variable with probability density 1 0
Problem 3. The random variable X has density function f given by 0,elsewhere (a) Assuming that θ-0.8, determine K (b) Find Fx(t), the c.d.f. of X (c) Calculate P(0.4sX s 0.8)
(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.
5. Find the moment generating function of the continuous random variable X whose a. probability density is given by )-3 or 36 0 elsewhere find the values of μ and σ2. b, Let X have an exponential distribution with a mean of θ = 15 . Compute a. 6. P(10 < X <20); b. P(X>20), c. P(X>30X > 10), the variance and the moment generating function of x. d.