5. A non-negative valued continuous random variable X satisfies P(X > x +y|X > x) =...
1. Given a continuous random number x, with the probability density P(x) = A exp(-2x) for all x > 0, find the value of A and the probability that x > 1.
Let X be an exponential random variable such that P(X < 27) = P(X > 27). Calculate E[X|X > 23].
X Y Z iid Suppose for random variable X, P(X > a) - exp( random variable Y, P(Y > y) exp(-0y) for y > 0, and for random variable , P(Z > z)--exp(-фа) for z > 0. (a) Obtain the moment generating functions of X, Y and Z. (b) Evaluate E(X2IX > 1) and show it is equal to a quadratic function of λ. (c) Calculate P(X > Y Z) if λ-1, θ--2 and φ--3. -λα) for x > 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.
Let X be an exponential random variable such that P(X<26) = P(X > 26). Calculate E[X|X > 28]. Answer: CHECK
3. Consider a continuous random variable X with pdf given by 0, otherwise This is called the exponential distribution with parameter X. (a) Sketch the pdf and show that this is a true pdf by verifying that it integrates to 1 (b) Find P(X < 1) for λ (c) Find P(X > 1.7) for λ : 1
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.
A continuous random variable Z is said to have a Laplace(H, b) distribution if its PDF is given by: where μ R and b > 0. a) Ifx-Laplace( 0, b-1), find E(X] and Var[X]. b) If X ~ Laplace(p = 0, b 1) and Y bX + μ, show that Y is a Laplace random variable. c) Let Z ~ Laplace(u, b), where μ E R and b > 0. Find E[2] and Var [2]
Please help me solve this differential Equation show all steps Find a continuous solution satisfying +y-f(x), where f() Ji 10 { 0<r<1 > 1 and y(0) -0.
For a continuous random variable X, P(27 ≤ X ≤ 74) = 0.35 and P(X > 74) = 0.10. Calculate the following probabilities. (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 2 decimal places.) For a continuous random variable X, P(27 sxs 74) = 0.35 and PIX> 74) = 0.10. Calculate the following probabilities. (Leave no cells blank - be certain to enter "O" wherever required. Round your answers to 2 decimal...