610] Prove that for an exponential distribution, the expected value of the distribution is
2. The exponential distribution with rate λ = 0.25. What is the expected value X ∼ Exp(λ = 0.25)? n = 400
2 Let X have an exponential distribution with parameter λ Verify the formulas for expected value and variance on the formula sheet.
X is a random variable with exponential distribution whose expectation is . Prove : We were unable to transcribe this imageた! E(Xk) =E, k = 1.2. 3
Losses follow an exponential distribution with mean 1. Two independent losses are observed. Calculate the expected value of the smaller loss.
A random variable X obeys the exponential distribution law xp-x),(20). m! Prove that the following inequality holds true:
X is a Laplace Distribution (Double Exponential Distribution) with mu = beta and b = alpha. f(x) = where alpha > 0 Derive an Expression for E(|X - E(X)|). (The expected value of the absolute value of X - the mean).
5. The Exponential(A) distribution has density f(x) = for x<0' where λ > 0 (a) Show/of(x) dr-1. (b) Find F(x). Of course there is a separate answer for x 2 0 and x <0 (c Let X have an exponential density with parameter λ > 0 Prove the 'Inemoryless" property: P(X > t + s|X > s) = P(X > t) for t > 0 and s > 0. For example, the probability that the conversation lasts at least t...
exponential distribution 3. The distribution of Smith's future lifetime is X, an exponential random variable with mean a, and the distribution of Brown's future lifetime is Y, an exponential random variable with mean B. Smith and Brown have future lifetimes that are independent of one another. Find the probability that Smith outlives Brown. Answer #3: (D) a (E) (A) (B) (C) 3. The distribution of Smith's future lifetime is X, an exponential random variable with mean a, and the distribution...
Prove that if T has an arbitrary continuous distribution, the cumulative hazard of T, A(T), has an exponential distribution with unit parameter.
Problem 5. Let X be a continuous random variable with a 2-paameter exponential distribution with parameters α = 0.4 and xo = 0.45, ie, ;x 2 0.45 x 〈 0.45 f(x) = (2.5e-2.5 (-0.45) Variable Y is a function of X: a) Find the first order approximation for the expected value and variance of Y b) Find the probability density function (PDF) of Y. c) Find the expected value and variance of Y from its PDF Problem 5. Let X...