Let U1, . . . , Un be a random sample from the Unif(0,1) distribution. (a) Find the distribution of Y1 = −2 log U1 . (b) Show that the distribution Y = −2 ∑ni=1 log Ui is χv2 for some value of ν. (c) What is the value of ν in part (b)?

Let U1, . . . , Un be a random sample from the Unif(0,1) distribution. (a) Find the distribution of Y1 = −2 log U1 . (b) Show that the distribution Y = −2 ∑ni=1 log Ui is χv2 for some value of ν. (c) What is the value of ν in part (b)?

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

Related questions

Q: 1. Suppose that X is a random variable with pdf: f(x) = (2x + 1)/6, 0 < x < 2. (a)Find the cdf…

Q: Q-2: Let X1, X2, ..., X, be independent, exponentially distributed random variables with mean ). 1.…

Q: (a) Is EX; sufficient for 0? (b) Find a complete sufficient statistic for 0.

Q: Q. 1 Let X be a random variable with the following mass distribution P(X = x) %3D 0.3 1 0.5 2 0.2…

Q: Let W be a plane in R³. Let P be the matrix of the projection onto W and let R be the matrix of the…

Q: An appropriate sampling time for the signal x(t)=cos(Tt)

A: Period of the signal is 2. So using Nyquist criterion the appropriate sampling time will be half of…

Q: Question: Please Calculate E(Y₂) Ci.e. Please calculate the expected value of y at t=2)

A: The question is about time series : Given : yt = 3t + ut + 4

Q: iid 2. Let Y1,..., Yn-1 xỉ and consider U = E Y;. n-1 i=1 (a) Show that U~ (b) What is the…

Q: (a) Write the expression for the auto correlation function Rn(T) of the white noise. (b) Write the…

A: Answer: For the given data,

Q: 4. Suppose that O is a uniform random variable on the interval (-1/2,1/2). Let T = tan 0. Find the…

A: Solution

Q: 5. Let X₁, X2,..., Xn are random samples from the pdf f(x; 0) = 0/x², 0 < 0≤x. a) Find the mle of 0.…

A: f(x;θ)=θx2;0<θ<x

Q: If Y is a random variable with moment generating function my (t)= e° , what is the mean of Y ?

A: Solution: Let Y be random variable with Moment generating function

Q: 3.155 Let m(t) = (1/6)e' + (2/6)e² + (3/6)e. Find the following: a E(Y) V (Y) The distribution of Y…

Q: (c) Compute the variance of X using its MGF.

Q: 2.6 Apply the inverse-transform method to generate random variables from a Laplace distribution…

Q: 2. Let U₁, U₂,... be IID Uniform(0, 1) random variables. Let M₁ = I₁U; be the product of the first n…

Q: A CI is desired for the true average stray-load loss ? (watts) for a certain type of induction motor…

Q: iid *1. Let Y₁,..., Yn uniform(0, 1). Find the distribution of their geometric mean: U = (ÎIx.)* ΠΥ…

Q: Let X₁, Xn be a random sample from the beta distribution with a = B = 0 and = = {0: 0= 1,2}. Show…

Q: Xn = a sin(bn + Z), n = Z, where a and b are positive constants and Z is a random variable with…

Q: The waiting time for the tenth customer to arrive to arrive at a pharmacy in a certain medical…

Q: Q.1. Let X= (Xı, ..Xn) be a random sample of random variables with probability density fe. Find an…

Q: 3. X(t) = A cos(2n fet +0) where A is a Rayleigh random variable independent of 0 which is a uniform…

Q: Q.3 The probability density function for a continuous random variable X is Sa + bx²; 0 s< x< 1,…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: Let U1, . . . , Un be a random sample from the Unif(0,1) distribution. (a) Find the distribution of…

A: The objective of the question is to find the distribution of a transformed random variable and to…

Q: generating functions shown below. For each random variable also indicate what the mean and the…

A: We know that the moment generating function uniquely specify the distribution. Note : According to…

Q: (a) Calculate the median of X. (b) Note: No need to show the second derivative. Calculate the mode…

Q: Question is attached.

A: Given thatThe moment generating function of a random variable isTo find mean and variance:

Q: Question is attached

A: (a)From the given information,

Q: Let X1, X2,..., X, be a set of independent random variables each following the distribution with pdf…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: 4.4 Two random variables, T₁ and T2, are independent and exponentially distributed according to…

A: In this problem, we have two identically and independently distributed (iid) random variables, and…

Q: Consider the following joint frequency function. Y 6 0.14 0.13 0.24 0.17 0.04 0.12 0.05 0.11

A: Solution: 1. The given joint frequency function is

Q: (x-μ)² 4(0²)² condition for deriving the estimator for the variance. Consider True alog L 062 False…

A: In statistical estimation, the first order condition for deriving the estimator for the variance…

Q: 1. Suppose a researcher goes to a small college of 200 faculty,12 of which have blood type O-…

A: Population size N=200Number of faculty members who have blood type-O negative in the population is…

Q: Q.1. Let X= (X1, .X.) be a random sample of random variables with probability density fo. Find an…

Q: The variable X has the distribution Exp(5N), i.e. it has the PDF f(x)3D5N25N* for x>0. The variable…

Q: generating functions: a m(t) = [(1/3)e' +(2/3)]5. e' h m(t).

A: Note: According to the Bartleby guidelines expert solve only one question and rest can be reposted.

Question

100%

Let U₁, . . . , U_n be a random sample from the Unif(0,1) distribution.

(a) Find the distribution of Y₁ = −2 log U₁ .
(b) Show that the distribution Y = −2 ∑ni=1 log Ui is χ_v² for some value of ν.

(c) What is the value of ν in part (b)?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given Information

VIEW

Step 2: Distribtion of Y1:

VIEW

Step 3: distribution of Y:

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

(52) Let X be a random variable with p.d.f. 1 0
30.Mathematical statistics
x² = EL i=1 (O₁ - E₁) ² Ei Prove that the above statistic follows a chi-square distribution with a determination of degrees of freedom
Consider a random sample X1,...,Xn (n > 2) from Beta(θ,1), where we wish to estimate the parameter θ. (a) Find the MLE θˆ and write it as a function of T = − ∑ni=1 log Xi. (b) Find the sampling distribution of T = − ∑ni=1 log Xi . (Hint: First find the distribution of Ti = − log Xi .)
Help
Of 120 Pharmacy freshman, 65 are taking Math-150 and 47 taking Physics. 20 students of the freshman are not enrolled in either class. a) How many students are enrolled in both classes? b) What is the probability that a freshman selected at random is enrolled in both classes?
4. Question 4: Y is a discrete random variable with PMF S1/3, y=1 p(y) = 2/3, y = 2 (a) Find the MGF for Y. (b) Develop the first two raw moments from MGF and find the variance V(Y). Answers:
Which of the following could be the correlation function of a stationary random process? (a) R(t) = exp(-7). (d) R(T) = sin(7). (b) R,(t) exp(-г)и( г). (e) R(7) = cos (r). %3D (c) R (7) = exp(l1). (f) R(7) = sinc(7). %3D
Question 1: Let X beta(a, 1). Find the distribution of- log(X). Hint: Use the fact that I'(a+1) = al(@)
Suppose claim amounts at a health insurance company are independent of one another. In the first year calim amounts are modeled by a gamma random variable X with alpha=40, and beta=3. In the second year, individual claim amounts are modeled by random variable Y=1.05X+3. Let W be the average of 30 claim amounts in year two set up the equation to model the random variable W. a) Find the moment generating function of W b) Based on moment generating function of W is W also a gamma distribution? if so what are the parameters? c) Find the approximate probability that W is between 125$ and 130$.
Find 1-4
3) Assume that a random variable X has moment generating function as follows: e' + e²¹ M(t)=4-2e¹ ∞ Calculate the mean and variance of X. for t