矩生成函数(Moment Generating Function, MGF)是用来寻找矩的函数的函数。随机变量实值函数 X 的MGF 定义为: ψX(t)=E(etX)=∫etxdF(x)=∫etxf(x)dx 其中t=0 表示一阶矩,t=1 表示二阶矩…… 它实际上是一个 Laplace 变换。 对于实变函数 x(t),其拉普拉斯变换是复变函数 X(s) (其中复变量 s=...
Let X have the γ distribution with parameters α and θ. 1. Find the moment-generating function of X. 2. Find the mean and variance using the MGF of X. Gamma Distribution: The gamma distribution is the general version of ...
Sometimes, it is easier to work with the moment generating function than with actual density functions or cumulative distribution functions. Answer and Explanation: The mgf of the random variable Y is given by: $$M_Y(t) = E(e^{tY})=E(e^{tX^2...
a) Find the pdf of Y, when the distribution of X is N(0, 1). b) Find the PDF of Y, when the PDF of X is f (x) = (3 / 2)x^2, -1 less than or equal to x less than 1.The pdf of a continuous random variable X is given by f(x) = { 1 / 4 ...