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)
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...
The moment generating function ф(t) of random variable X is defined for all values of t by et*p(x), if X is discrete e f (x)dx, if X is continus (a) Find the moment generating function of a Binomial random variable X with parameters n (the total number of trials) and p (the probability of success). (b) If X and Y are independent Binomial random variables with parameters (n1 p) and (n2, p), respectively, then what is the distribution 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
(1 point) If X is a random variable with moment generating function ui) = (1-1)-9, t < I/7 then E(X) = and Var(X) =
6. Suppose the moment generating function of a random variable X is My(t) = (1 – 2+)-3, fort € (-1/2,1/2) Use this to determine the mean and variance of X.
(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.
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]
If the discrete random variable X has a moment generating function given by My(t) = (e'-1) Find E(X + 2x2) and Var(2X + 40).
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?