The random variable X follows a two-parameter Pareto with coefficient of variation 1.5. Determine the coefficient of skewness of X .
The random variable X follows a two-parameter Pareto with coefficient of variation 1.5. Determine the coefficient...
If X follows a two-parameter Pareto distribution with a = 3 and θ = 100, find the density function of Y, where Y- 1.5X
3. X is the random variable for claim sizes. Given A, X follow a single-parameter Pareto distribution with parameters θ 1000 and A. The distribution of A over the entire population is an exponential distribution with mean 3 Calculate Pr(X> 1500)
A discrete random variable X follows the geometric distribution with parameter p, written X ∼ Geom(p), if its distribution function is A discrete random variable X follows the geometric distribution with parameter p, written X Geom(p), if its distribution function is 1x(z) = p(1-P)"-1, ze(1, 2, 3, ). The Geometric distribution is used to model the number of flips needed before a coin with probability p of showing Heads actually shows Heads. a) Show that fx(x) is indeed a probability...
The random variable X is distributed as a Pareto distribution with parameters α = 3, θ. E[X] = 1. The random variable Y = 2X. Calculate V ar(Y )
Two questions exist : ) if it has pdf. A railon variable X has the l'areio distril illi ribution with parameters m, a (m, α > 0 w 0 otherwise Show that if X has this Pareto distribution, then the random variable log(X/m) has the expo- nential distribution with parameter α Let X ~ Gamma(α, β), where α > 1 . Find E[1/X]. ) if it has pdf. A railon variable X has the l'areio distril illi ribution with parameters...
X is a Poisson random variable of parameter 3 and Y an exponential random variable of parameter 3. Suppose X and Y are independent. Then A Var(2X + 9Y + 1) = 22 B Var(2X + 9Y + 1) = 7 CE[2X2 + 9Y2] = 19 D E[2X2 + 9Y2] = 26
3. Let X be an exponential random variable with parameter 1 = $ > 0, (s is a constant) and let y be an exponential random variable with parameter 1 = X. (a) Give the conditional probability density function of Y given X = x. (b) Determine ElYX]. (c) Find the probability density function of Y.
Problem 4. X, a Marvell-Bolzman random variable with parameter σ2, has pdf otherwise Determine the value of the constant c so that f(x) is a proper pdf.
Problem The random variable X is exponential with parameter 1. Given the value r of X, the random variable Y is exponential with parameter equal to r (and mean 1/r) Note: Some useful integrals, for λ > 0: ar (a) Find the joint PDF of X and Y (b) Find the marginal PDF of Y (c) Find the conditional PDF of X, given that Y 2. (d) Find the conditional expectation of X, given that Y 2 (e) Find the...
Coefficient of Variation The coefficient of variation standardizes a variable's dispersion (standard deviation) relative to its mean. Imagine two variables, each with a standard deviation of 20. If Variable 1 has a mean of 100 and Variable 2 has a mean of 10, it is obvious that has more relative uncertainty. The coefficient of variation, the amount of risk per unit of the mean, is found by dividing the standard deviation by the mean, as follows: CV = Standard Deviation...