Plz solve correctly plz ? Let X₁, X₂, ..., X, be independent exponentialrandom variables with parameter 1.a. Find the moment-generating function ofY = X₁ + X₂ + + X₁.b. What is the distribution of the randomvariable Y?My(t)=(₁²₁); betatdistributionMy(t)=(²); PoissonrdistributionrMy(t)=(₁=1)distributionMy(t):(₁4₁)+ tdistributionMy(t)=(²)distributionO=; normal; binomial; gamma

Given : X1,X2.....Xr be independent exponential random variables with parameter λ we have to find…

Answered: a. Find the moment-generating function…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

If X is exponentially distributed with parameter λ and Y is uniformly distributed on the interval [a, b], what is the moment generating function of X + 2Y ?
If we let RX(t) = ln MX(t), show that R X(0) = μ and RX(0) = σ2. Also, use these results to find the mean and the variance of a random variable X having the moment-generating function MX(t) = e4(et−1)
Let X1, . . . , Xn be iid with pdf f(x) = 1 x √ 2πθ2 e − (log(x)−θ1) 2 2θ2 , −∞ < x < ∞, and unknown parameters θ1 and θ2. Find the maximum likelihood estimators for θ1 and θ2, respectively
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.
Theorem 6.4 states that the moment-generating function of the gamma distribution is given by Mx(t) = (1-βt)^(-α).
The following facts about a company are known: 1. At present, its total capital is £3 million. 2. It has just sold zero-coupon bonds with the total nominal value of £2 million which it promises to repay in 18 months from now. 3. The total capital F(t) of the company follows the geometric Brownian motion with parameters µ = 0.15 and σ = 0.2. The continuously compounded annual interest rate r = 6%. Within the framework of the Merton model, establish the following. (c)What is the probability that the company would default on its promise to bond holders?
Consider two securities, the first having μ1 = 1 and σ1 = 0.1, and the secondhaving μ2 = 0.8 and σ2 = 0.12. Suppose that they are negatively correlated,with ρ = −0.8. Denote the expected return and its standard deviation as functions of π byμ(π ) and σ (π ). The pair (μ(π ), σ (π )) trace out a curve in the plane as πvaries from 0 to 1. Plot this curve in R.
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
Let i_t denote the effective annual return achieved on an equity fund achieved between time (t -1) and time t. Annual log-returns on the fund, denoted by In(1 + i_t) , are assumed to form a series of independent and identically distributed Normal random variables with parameters u = 6% and o = 14%.An investor has a liability of £10,000 payable at time 15. Calculate the amount of money that should be invested now so that the probability that the investor will be unable to meet the liability as it falls due is only 5%. Using only formulas, no tables
I need helping finding the Jeffreys’ prior for the parameter alpha of the Maxwell distribution and then finding a transformation of this parameter in which the corresponding prior is uniform.
Let X1 ... Xn i.i.d random variables with Xi ~ U(0,1). Find the pdf of Q = X1, X2, ... ,Xn. Note that first that -log(Xi) follows exponential distribuition.
Consider the time series xt = β1 + β2t + wt, where β1 and β2 are known constants and wt is a white noise process with variance σ2 w. (a) Determine whether xt is stationary. (b) Show that the process yt = xt − xt−1 is stationary. (c) Show that the mean of the moving average vt = 1 2q + 1 q j=−q xt−j is β1 + β2t, and give a simplified expression for the autocovariance function.

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS

a. Find the moment-generating function of Y = X₁ + X₂ + ... + X₁. b. What is the distribution of the random variable Y?