Just B please 5. Suppose that X₁,..., Xn form a random sample from an exponential distribution with rate X,whose PDF is-xxƒ(x|X) = Ae¯¤, for x > 0, λ > 0.Gamma(n, A) with PDFIt can be shown that Σ₁ X₁ ~XiInI(n)By the property of Gamma distributions, it follows thatf(x|n, x)=n20 ΣΧ ~ Gammai=1xn-¹e-xx2n 122= x²(2n).(a) Based on the fact that 2X₁ X; ~ x²(2n), derive a (1 − a) × 100% confidence interval2λfor X.(b) Suppose that we have observed the following data of n = 87.8 2.4 3.0 20.0 4.2 4.8 7.4 6.7from exponential (X). Construct a 95% confidence interval for A based on the formula thatyou have derived in Part (a).

Answered: whose PDF is η «η IULIII d Oill sa ле…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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X is an exponential random variable with λ =1 and Y is a uniform random variable defined on (0, 2). If X and Y are independent, find the PDF of Z = X-Y2
Suppose that X is a continuous unknown all of whose values are between -3 and 3 and whose PDF, denoted f , is given by f ( x ) = c ( 9 − x^2 ) , − 3 ≤ x ≤ 3 , and where c is a positive normalizing constant. What is the variance of X?
Suppose that X is a continuous unknown all of whose values are between -5 and 5 and whose PDF, denoted f, is given by f ( x ) = c ( 25 − x^2 ) , − 5 ≤ x ≤ 5 , and where c is a positive normalizing constant. What is the expected value of X^2?
Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample? I asked this question earlier today, but didn't quite understand all of the response. P(y1<=yn)p(y2<=yn) and so on was used, but shouldn't the yn be listed first in the inequality since we want to know if yn is the smallest?
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2) The time between successive customers coming to the market is assumed to have Exponential distribution with parameter l. a) If X1, X2, . . . , Xn are the times, in minutes, between successive customers selected randomly, estimate the parameter of the distribution. b) b) The randomly selected 12 times between successive customers are found as 1.8, 1.2, 0.8, 1.4, 1.2, 0.9, 0.6, 1.2, 1.2, 0.8, 1.5, and 0.6 mins. Estimate the mean time between successive customers, and write down the distribution function. c) In order to estimate the distribution parameter with 0.3 error and 4% risk, find the minimum sample size.
If X is a random variable that is uniformly distributed between -1 to 1, find the PDF √|X| of and pdf of -ln|X|
Let X1, X2 denote two independent variables, each with a x^2(2) distribution. Find the joint pdf of Y1=X1 and Y2 = X2+X1. Note that the support of Y1, Y2 is 0<y1<y2<infinity. Also, find the marginal pdf of wach Y1 and Y2. Are Y1 and Y2 independent?
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LetX1,X2,...,Xn be a sequence of independent and identically distributed random variables having the Exponential(λ) distribution,λ >0, fXi(x) ={λe−λx, x >0 0, otherwise Define the random variable Y=X1+X2+···+Xn. Find E(Y),Var(Y)and the moment generating function ofY.

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