Show that, if the random variable X has an F-distribution with ν1 and ν2 degrees of freedom, then Y = 1 X has an F-distribution with ν2 and ν1 degrees of freedom.

For a random variable X, suppose that E[X] = 1 and Var(X) = 5. Then %3D (a) E[(2 + X)²] = (b) Var(2 + 3X) = Netsu rtiol orodit on this problem

Without using a moment generating function; Prove that the variance of a beta-distributed random variable with parameters α and β is σ2 = αβ/[(α + β)^2 (α + β + 1)]

Consider a random variable V modeling the version of the software that people have installed on their computers, where the possible versions are {1, 2, 3, 4}. People are equally likely to have versions 1 and 2 and also equally likely to have versions 3 and 4. People are also x times more likely to have version 3 than version 2. (a) What is the (probability mass function) PMF of V as a function of x (b) What is the expected version of the software. Hint: the expected value of V as a function of x (c) What is the minimum value of x to ensure that the mean version is at least version 3?

If the number X of particles emitted during a 1-hour period from a radioactive source has a poisson distribution with parameter equal to 4 and that the probability that any emitted is recorded is p=0.9 find the probability distribution of the number Y of the particles recorded in a 1-hour and hence the probability that no particle is recorded