Q3. Assume that X is a continuous and nonnegative random variable with the cumulative distribution function...
Q3. Assume that X is a continuous and nonnegative random variable with the cumulative distribution function Fx Let b> o. (a) Find the cumulative distribution function of Y = (X-b)+ b) Apply the general formula from (a) to Pareto distribution with parameter a > 0. Hint: Consider separately cases b e (0, 1 and b> 1
Q2. Assume that X is a continuous and nonnegative random variable with the cumulative distribution function Fx Let b> 0. (a) Find the cumulative distribution function of Y = XI(X < b} (b) Apply the general formula from (a) to exponential distribution with parameter λ > 0.
Q2. Assume that X is a continuous and nonnegative random variable with the cumulative distribution function Fx. Let b > 0 a) Find the cumulative distribution function ofY -XKX< (b) Apply the general formula fron (a) to exponential distribution with parameter > 0.
Q2. Assume that X is a continuous and nonnegative random variable with the cumulative distribution function F and density f. Let b>0. (a) Write the formula for EXI(X < . (b) Apply the general formula from (a) to Pareto distribution with parameter α > 0.
Q1. Assume that X is a continuous and nonnegative random variable with the cumulative distribution function F and density f. Let b>0. (a) Write the forinula for E(X b)+1. (b) Apply the general formula from (a) to exponential distribution with parameter λ > 0.
Q4. Assume that X is a continuous and nonnegative random variable with the cumulative distribution function Fx Find the quantile function of Y-log(X)
Q4. Assume that X is a continuous and nonnegative random variable with the cumulative distribution function Fx Find the quantile function of Y -log(X)
Q1. Assume that X is a continuous and nonnegative random variable with the cumulative distribution function Fx and density fx, and let c>O. Verify that for the Value-at-Risk we have VaR,x (p) = cVaRx (p)
Question 3: Let X be a continuous random variable with cumulative distribution function FX (x) = P (X ≤ x). Let Y = FX (x). Find the probability density function and the cumulative distribution function of Y . Question 3: Let X be a continuous random variable with cumulative distribution function FX(x) = P(X-x). Let Y = FX (x). Find the probability density function and the cumulative distribution function of Y
The cumulative distribution function for a continuous random variable X is given by 0, S 0 F(x) = 1, r 21. (a) Find the density fx for X. (b) Find the mean ? and variance ?2 for X.