Suppose Y1,Y2,··· ,Yn are i.i.d. continuous uniform(0,1) distributed. (a) Prove that the kth-order statistic, Y(k), has Beta distribution with α = k and β = n−k+ 1. (b) What is the distribution of the median of Y1,Y2,··· ,Yn when n is an odd integer? (c) Find the joint density of the middle two of Y(1),Y(2),··· ,Y(n) when n is an even integer

Suppose Y1,Y2,··· ,Yn are i.i.d. continuous uniform(0,1) distributed. (a) Prove that the kth-order statistic, Y(k), has Beta distribution with α = k and β = n−k+ 1. (b) What is the distribution of the median of Y1,Y2,··· ,Yn when n is an odd integer? (c) Find the joint density of the middle two of Y(1),Y(2),··· ,Y(n) when n is an even integer

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Suppose that the continuous two-dimensional random variable (X, Y ) is uniformly distributed over the square whose vertices are (1, 0), (0, 1), (−1, 0), and (0, −1). Find the Correlation Coefficient ρxy
Find the sampling distributions of Y1 and Yn for ran-dom samples of size n from a population having the beta distribution with α = 3 and β = 2.
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.
Suppose that the random variables X1,...,Xn form a random sample of size n from the uniform distribution on the interval [0, 1]. Let Y1 = min{X1,. . .,Xn}, and let Yn = max{X1,...,Xn}. Find E(Y1) and E(Yn).
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
A poisson random variables has f(x,3)= 3x e-3÷x! ,x= 0,1.......,∞. find the probabilities for X=0 1 2 3 4 and also find mean and variance from f(x,3).?
Suppose that three random variables X1, X2, X3 form a random sample from the uniform distribution on interval [0, 1]. Determine the value of E[(X1-2X2+X3)2]
Let Y1, Y2, ... , Yn be a random sample of size n from a gamma distribution with parameters α = 1and β = 2. Derive the probability distribution of the sample mean Y̅ using moment-generatingfunctions.
Suppose the random variable y is a function of several independent random variables, say x1,x2,...,xn. On first order approximation, which of the following is TRUE in general?
Let X1, X2, ..., X10 be a random sample from a gamma distribution with α = 3 and β = 1/θ. Suppose we believe that theta follows a gamma-distribution with α = 28 and β = 17 and suppose we have a trial (X1 , ... , Xn ) with an observed x̄ = 28.2 What is the posterior distribution of θ What is the Bayes point estimate of θ associated with the square-error loss function?
If Y is a continuous, uniformly distributed random variable over the interval(4,10), then the value of the PDF between 4 and 10 is?
Suppose the distribution of the time $X$ (in hours) spent by students at a certain university on a particular project is gamma with parameters $\alpha=50$ and $\beta=2 .$ Because $\alpha$ is large, it can be shown that $X$ has approximately a normal distribution. Use this fact to compute the approximate probability that a randomly selected student spends at most 125 hours on the project.