If E(Xr) = 6, r = 1,2,3, , find the moment generating function M(t) of X...
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
7. Derive the moment-generating function M(t) for X 1(a, X). 8. Expand the moment-generating function M(t) = ex+oft®/2 in a power series in t to compute E[X3] if X ~ N(1, 2).
Suppose that the moment generating function of X is M(t) 1-2t . Find E[X]rounded to nearest .xx.
Suppose that the moment generating function of X is M(t) 1-2t . Find E[X]rounded to nearest .xx.
Let X U(0,theta). Find the moment generating function of X and show how to use it to find the mean and variance of X.I think this follows the uniform distribution so..mean = (theta1 + theta2)/2variance = [(theta2- theta1)^2]/ 12moment generating function = [e^(t*theta2) - e^(t*theta1)]/(t * (theta2-theta1))I think the beginnning of the problem means that theta1 is 0? I'm not sure how to show the moment generating function.
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?
If the moment-generating function of a random variable X is M(t)=(1/6)et+(1/3)e2t+(1/2)e3t, (a) Find the mean of X (b) Find E[1/X] (c) Find Var(X)
Suppose the moment generating function of X is M(t) = z 1 2-et Find E[X2]
Suppose the moment generating function of X is M(t) = z 1 2-et Find E[X2]
Suppose the moment generating function of X is M(t) = z 1 2-et Find E[X2]