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

C1. Let X be a continuous random variable with PDF f(x) = (2-x) ² for -1 1)? (c) Calculate the expectation of X. (d) Calculate the variance of X.

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.

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 io patients are admitted and X denotes the number of patients diagnosed with this type of cancer. The mean and the variance of X are: E(X)=0.4 and V(X)=0.384 O None of these O E(X)=0.5 and V(X)=0.475 O E(X)=0.3 and V(X)=0.291

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

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 it was XG (23) Independent of Xen G (13) Find Miley D-Probability density Function of the Variable YaX+Xq 2 -the Mean variance of the variable

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.

The velocity of a particle in a gas is a random variable X with probability distribution fx(x) = 32x²e-4x The kinetic energy of the particle is Y = 1/mX². Suppose that the mass of the particle is 64 yg. Find the probability distribution of Y. (Do not convert any units.) x >0.

Find the value of c, the expectation of X, and the variance of X.