(1 point) If X is a random variable with moment generating function then and Var(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) =
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).
1. Using the appropriate moment generating,function. Show that Var(X)-: ? when Poisson distribution with mean ?. X has the ting function of the random variable with probability density function
(1 point) Suppose that the moment generating function of a random variable X is My(t) = exp(4e – 4) and that of a random variable Y is My(t) = ( oer + 3)''. If X and Y are independent, find each of the following. (a) P{X + Y = 2} = (b) P{XY = 0} = (c) E[XY] = (d) E[(X+Y)?] =
Let X be a discrete random variable. If the moment generating function of X is given by (1 -0.9+0.9e) 15. The first moment of X is Hint: Write the answer with one decimal point. Answer.
Let X be a discrete random variable. If the moment generating function of X is given by (1 – 0.6 + 0.6e')? The first moment of X is 8 Hint: Write the answer with one decimal point. Answer:
(3 points) The random variable X has moment generating function px(t) = (0.55e +1 – 0.55) Provide answers to the following to two decimal places (a) Evaluate the natural logarithm of the moment generating function of 4X at the point t = 0.11. (b) Hence (or otherwise) find the expectation of 4X. (c) Evaluate the natural logarithm of the moment generating function of 4X + 8 at the point t = 0.11. Note: You can earn partial credit on this...
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)
(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.
3.81 The random variable X has moment generating function M (1) = 0.2e41 + 0.7e7t + 0.1 e9t -oo < t <00, Find P(X = 7).