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).
X is a Laplace Distribution (Double Exponential Distribution) with mu = beta and b = alpha....
The Laplace distribution (also known as the double-exponential distribution) is a continuous distribution with location parameter m ER and density given by fm (x) = fe e-ml. Let X denote a Laplace random variable with location parameter set to be m = 0. What is E[X]? Does the variance o2 = E[(x – E[X])21 exist? Yes No Which of the following are true about X? (Choose all that apply.) Hint: The function chez is integrable, i.e. L ke-12 dc is...
Problem #3. X is a random variable with an exponential distribution with rate 1 = 3 Thus the pdf of X is f(x) = le-ix for 0 < x where = 3. a) Using the f(x) above and the R integrate function calculate the expected value of X. b) Using the dexp function and the R integrate command calculate the expected value of X. c) Using the pexp function find the probability that .4 SX 5.7 d) Calculate the probability...
Let X be a random variable with finite mean mu and such that E[(X - mu)^2] is finite. Then the variance of X is defined to be E[(X - mu)^2], denoted as sigma^2. Using this expected value expression: sigma^2 = E[(X - mu)^2], show that the variance, sigma^2 = E(X^2) - mu^2
QUESTION 4 The bivariate beta type Il distribution has the probability density function a-1,b-1 x>0, y>0 (1+x+y)atbte, where K 「(a)「(b)「(c) = (a) Derive the marginal probability density function of X (5 (b) Find the E (XYs) (5
QUESTION 4 The bivariate beta type Il distribution has the probability density function a-1,b-1 x>0, y>0 (1+x+y)atbte, where K 「(a)「(b)「(c) = (a) Derive the marginal probability density function of X (5 (b) Find the E (XYs) (5
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...
A random varible X taking values from [0,1] has Beta distribution of parameters a and B, which we denote by Beta(a,b), if it has PDF _f(a+B) fa-1(1 – X)B-1, fx(x) = T(a)l(B) where I(z) is the Euler Gamma function defined by I(z) = Sx2-1e-*dx. Bob has a coin with unknown probability of heads. Alice has the following Beta prior: A = Beta(2,3). Suppose that Bob gives Alice the data on = {x1,...,xn), which is the outcome of n indepen- dent...
2. Suppose XX2,X is a random sample from an exponential distribution with . Let X(1) minX1,X2, Xn), the minimum of the sample mean (a) Show that the estimator 6nx is an unbiased estimator of 8. (hint: you were asked to derive the distribution of X for a random sample from an exponential distribution on assignment 2 -you may use the result) (b) X, the sample mean, is also an unbiased estimator of . Which of the unbiased estimators, or X,...
Gamma, Exponential, Weibull and Beta Distributions (Part
3)
1. The random variable X can modeled by a Weibull distribution with B = 1 and 0 = 1000. The spec time limit is set at x = 4000. What is the proportion of items not meeting spec? 2. Suppose that the response time X at a certain on-line computer terminal (the elapsed time between the end of a user's inquiry and the beginning of the system's response to that inquiry) has...
70.If X has an exponential distribution with parameter ⋋, derive a general expression for the (100p)th percentile of the distribution. Then specialize to obtain the median.