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.

Get the variance and standard deviation

The p.d.f. of a random variable X' is as shown in the figure. The pdf is zero for X 5. Calculate (i) the maximum value of p.d.f. (ii) expectation of X, E(X) (iii) variance of X. fx (x) k

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

Suppose that the probability that a patient admitted in a hospital is diagnosed with a certain type of cancer is 0.03. Suppose that on a given day 10 patients are admitted and X denotes the number of patients diagnosed with this type of cancer. The mean and the variance of X are: None of these E(X)=0.5 and V(X)=0.475 E(X)=0.4 and V(X)=0.384 E(X)=0.3 and V(X)=0.291

U is a uniform (0, 1) random variable and X = −ln(1 − U). Find the PDF, CDF of randomvariable X. Calculate the expected value of X.

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.