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6. Given ?c(x+1) if1<x<3 0 else as a probability function for a continuous random variable; find a. the constant c. b. The moment generating function MX(t). c. Find the variance and the standard deviation 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.
(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.
Use the given moment-generating function, Mx(t), to identify the distribution of the random variable, X in each of the following cases. (Specify the exact type of distribution and the value(s) of any relevant parameters(s): 1. (a) M(-3 (b) M() exp(2e -2) Ce) M T112t)3 (f) Mx(t) = ( 1-3t 10 ) (d) Mx(t)= exp(2t2_t) (e) Mx(t)= - m01 -2t)!
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.
A random variable has a moment generating function given by MX(t) = (e^t + 1)^4/16 . Find the expected value and the variance of the variable Y = 2X + 3
The moment generating function (MGF) for a random variable X is: Mx (t) = E[e'X]. Onc useful property of moment generating functions is that they make it relatively casy to compute weighted sums of independent random variables: Z=aX+BY M26) - Mx(at)My (Bt). (A) Derive the MGF for a Poisson random variable X with parameter 1. (B) Let X be a Poisson random variable with parameter 1, as above, and let y be a Poisson random variable with parameter y. X...
Let X be a continuous random variable with values in [ 0, 1], uniform density function fX(x) ≡ 1 and moment generating function g(t) = (e t − 1)/t. Find in terms of g(t) the moment generating function for (a) −X. (b) 1 + X. (c) 3X. (d) aX + b.
The moment generating function of a random variable X is as follows: 1-Xt Find the probability that X is within 0.5 standard deviation from its mean.
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.
problem 3 and 4 please. 3. Find the moment generating function of the continuous random variable & such that i f(x) = { 2 sinx, Ox CT, no otherwise. 4. Let X and Y be independent random variables where X is exponentially distributed with parameter value and Y is uniformly distributed over the interval from 0 to 2. Find the PDF of X+Y.