7-47. Consider the shifted exponential distribution When θ=0, this density reduces to the usual exponential dis-...
Exponential(). That is Y has a density function of the form 7. Let Y Ay f(y) = de"^9,y> 0 where 0. Show that: (a) If a >0 and b > 0, then P(Y > a + b|Y > a) = P(Y > b) (b) E(Y) 1/A
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)
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...
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.
4. Consider the probability density function (x)for x>0, and zero otherwise. Determine a. The value of a b. P(X> 22) C. e The value of x such that P(X<x)-0.1
2. Suppose X1, X2, . .., Xn are a random sample from θ>0 0, otherwise Note: If X~fx(a; 0), thenXEx(0). (a) Find the CRLB of any unbiased estimator of θ (b) Is the MLE for θ the MVUE?
n. 7. Let Xi, , Xn be iid ;0) =-e-r2/0 where x > 0. Sho w that θ=「x? is based on f (x efficient.
2. The probability density function of X is given by 10 0,x < 10 a) Find P(X>20). b) What is the cumulative distribution function of X?
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.
The density of the charge distribution with spherical symmetry capability is: OSTSR- Por Py = R Py = 0, r>Re Find Ē at all point (use gauss law)