Find the expected value E(X) and the variance V(X) for the following probability density function. f(x) = 2x4 for 1

Given the probability density function f(x)=16f(x)=16 over the interval [2,8][2,8], find the expected value, the mean, the variance and the standard deviation.

b. Find E[X(X – 1)] for Poisson random variable. Use the result to find the variance of X.

Given the probability density function f(x)=15f(x)=15 over the interval [3,8][3,8], find the expected value, the mean, the variance and the standard deviation.Expected value:   Mean:   Variance:   Standard Deviation

Please help me with this problem. ASAP! within 2hours. Show complete and explicit step and don't skip any mathematical solution.   Consider a probability density function (PDF), where f(T-t) is a general function, g(T) and h(t) are time-dependent functions. (a) Calculate the first moment of the PDF. (b) Calculate the second moment of the PDF. (c) Calculate the variance.

Pb (Z = z) = B (8.25z - z2) with z E {1, 2, ......, 5}.   Find the mean and variance of Z using the probability mass function equation above.

A random variable Y has a uniform distribution over the interval (?1, ?2). Derive the variance of Y. Find E(Y)2 in terms of (?1, ?2). E(Y)2 =    Find E(Y2) in terms of (?1, ?2). E(Y2) =    Find V(Y) in terms of (?1, ?2). V(Y) =

If probability density function of a random varíable X is f(x) = x² for –1SXS1, and %3D O for any other value of x %3D is then, the percentage probabilityP

The proportion of people who respond to a certain​ mail-order solicitation is a random variable X having the following density function.   ​f(x) = 2(x+3)/7, 0<x<1, 0, elsewhere   Find the variance of X.

White-tailed does upon reaching sexual maturity at age two give birth to between one and four offspring every year. Below is the probability density function for live births in mature white-tailed does in optimal habitat.   Find the a) cumulative density function, b) mean c) variance for this probability density function.