The moment generating function of a random variable X is as follows: 1-Xt Find the probability...
(3 marks) The moment generating function of a random variable X is given by MX(t) = 24 20 < - In 0.6. Find the mean and standard deviation of X using its moment generating function.
Let be a random variable with probability density function f(x) and moment-generating function 1 1 M(t) = =+ = ? 6 . 6 1 + - 1 36 + -e a) Calculate the mean = E(X) of X b) Calculate the variance o? = E(X -w' and the standard deviation of X
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.
Question 18: a) Compute the moment generating function, MGF, of a normal random variable X with mean µ and standard deviation σ. b) Use your MGF from part a) to find the mean and variance of X.
Given f(x) = ( c(x + 1) if 1 < x < 3 0 else as a probability function for a continuous random variable; find a. c. b. The moment generating function MX(t). c. Use MX(t) to find the variance and the standard deviation of X.
For the probability density function f defined on the random variable x, find (a) the mean of x, (b) the standard deviation of x, and (c) the probability that the random variable x is within one standard deviation of the mean. f(x) = 1 30 x, [2,8] a) Find the mean. u = (Round to three decimal places as needed.) b) Find the standard deviation. = (Round to three decimal places as needed.) c) Find the probability that the random...
(4 marks The moment generating function (mgf) of a random variable X is given by (a) Use the mgf to find the mean and variance of X (b) What is the probability that X = 2?
If the moment generating function of X is 1/(1−2t), find the expected value of the random variable Y= 100(0.5)^X.
Exercise 1 Let X be a random variable that has moment generating function My(t) = 0.5-t2-t Find P[-1<x< 1]
6. (4 marks) The moment generating function (mgf) of a random variable X is given by m(t)-e2 (a) Use the mgf to find the mean and variance of X (b) What is the probability that X-2?