X is exponential random variable with λ = 3. A) Calculate E(X"2) of this random variable....
3. If X is an exponential random variable with parameter λ > 0, show that for c > 0 cX is exponential with parameter λ/c.
Let x be an exponential random variable with λ = 0.7. Calculate the probabilities described below. a. P(x < 4) P(x < 4) = ______ . (Round to four decimal places as needed.) b. P(x > 8) P(x > 8) = ______ . (Round to four decimal places as needed.) c. P(4 ≤ x ≤ 8) P(4 ≤ x ≤ 8) = ______ . (Round to four decimal places as needed.) d. P(x ≥ 3) P(x ≥ 3) = ______...
Let x be an exponential random variable with λ = 0.7. Calculate the probabilities described below. a. P(x < 4) P(x < 4) = ______. (Round to four decimal places as needed.) b. P(x > 8) P(x > 8) = ______ . (Round to four decimal places as needed.) c. P(4 ≤ x ≤ 8) P(4 ≤ x ≤ 8) = ______ . (Round to four decimal places as needed.) d. P(x ≥ 3) P(x ≥ 3) = ______ ....
Let X be exponential random variable with λ = 1. (a) Define Y = √ X. Specify the support of Y and find its density. (b)Define Z = X^2 + 2X. Specify the support of Z and find its density.
Let X be an exponential random variable with parameter λ, so fX(x) = λe −λxu(x). Find the probability mass function of the the random variable Y = 1, if X < 1/λ Y = 0, if X >= 1/λ
Suppose that T is an Exponential (λ=1) random variable and f(x)≐⌊x⌋ i.e. is the largest integer not more than x. Find the cdf and pmf for X≐f(T). What is E[f(T)]?
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...
(1) Let X be exponential random variable with λ = 1. (b) (6 pts) Define Z = X^2 + 2X. Specify the support of Z and find its density. Show all of your work and computations
Let X be an exponential random variable such that P(X<26) = P(X > 26). Calculate E[X|X > 28]. Answer: CHECK
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...