Exponential(). That is Y has a density function of the form 7. Let Y Ay f(y)...
Let Y be a random variable with probability density function, pdf, f(y) = 2e-2y, y > 0. Determine f (U), the pdf of U = VY.
7-47. Consider the shifted exponential distribution When θ=0, this density reduces to the usual exponential dis- tribution. When θ>0, there is positive probability only to the right of θ.
6. Write the pdf fy(y; 1) = le-dy, y> 0 in exponential form (see previous problem) and find a sufficient statistic for 1, assuming we have a sample of size n from this pdf.
Find the probability that Y is greater than 3.
Let Y have the probability density function f(y) = 2/y3 if y> 1, f(y) = 0 elsewhere.
11. Let X be a continuous random variable with density function fare-102 for 10 f(1) = lo otherwise where a > 0. What is the probability of X greater than or equal to the mode of X?
5. Let X have exponential pdf λe_AE 0 when x > 0 otherwise with λ = 3. Let Y-LX). Find E(Y) and Var(Y)
The Rayleigh density function is given by 2y) -y2 е ө y >0 f(y) = --{@ elsewhere The quantity Y? has an exponential distribution with mean o. If Yı, Y2, ..., Yn denotes a random sample from a Rayleigh distribution, show that Wn = ?=1 Y/? is a consistent estimator for e.
Let random variable X follows an exponential distribution with probability density function fx (2) = 0.5 exp(-x/2), x > 0. Suppose that {X1, ..., X81} is i.i.d random sample from distribution of X. Approximate the probability of P(X1+...+X81 > 170). A. 0.67 B. 0.16 C. 0.33 D. 0.95 E. none of the preceding
Suppose X and Y are independent random variables with Exponential(2) distribution (Section 6.3). We say X ~ Exponential(2) if its pdf is f(x) = -1/2 for x > 0.
PART V: Recall that for scalar > 0, the probability density function of an "exponential" random variable with parameter , is P2; 1) = exp(-x). We have n independent samples 11,..., Ir. Each 21, ..., Iris a scalar. Each ris an "exponential" random variable with parameter A. for which 12) (1 point] What is the maximum likelihood estimator? In other words, what is the value of the derivative of (D;) with respect to X is zero? Show all the steps...