Q2. 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 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 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.
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.
Q3. 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- (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.
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)
(15 points) Let X be a continuous random variable with cumulative distribution function F(x) = 0, r <α Inr, a< x <b 1, b< (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
2.5.9. The random variable X has a cumulative distribution function for xo , for xsO . for r>0 F(x) = z? 1 +x2 Find the probability density function of X.
2.5.9. The random variable X has a cumulative distribution function for xo , for xsO . for r>0 F(x) = z? 1 +x2 Find the probability density function of X.
12. (15 points) Let X be a continuous random variable with cumulative distribution function **- F() = 0, <a Inx, a < x <b 1, b<a (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)