Let X, i=1,.,20 be identical independent Poisson RVs distributed with parameter 1 = 2. Calculate andapproximation to P{Ei", ×, > 25}.

Answered: Image /qna-images/answer/bf60dbf8-4714-44f8-b241-ac8a6f93fb0a.jpg

Answered: Let X, i=1,.20 be identical independent…

Let X, i=1,.20 be identical independent Poisson RVs distributed with parameter i = 2. Calculate and approximation to P{E, X; > 25}.

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

Related questions

Q: Suppose that X is uniformly distributed on [0, 4]. Define Y = 2X + 5. Compute the pdf and cdf of Y.

Q: Let x1, ., Xn be a random sample with pdf is given by S(B + 1)xP, 0<x<1 f(x) = 0, %3D otherwise.…

Q: Let X1, ... , Xn be a random sample have the pdf 1 (1-0) f(x,0) = -(x),0 < x < 1, 0<0 < ∞. Find mle…

A: The likelihood of X1,X2,...,Xn is given as: L=∏i=1nfxi,θ=∏i=1n1θxi1-θθ=1θ∏i=1nxi1-θθ…

Q: X is known to follow the Beta distribution with the parameter 0 = 1000, a = 2, b = 1. wwwww Define…

Q: Let Y1 < Y2 < Y3 be the order statistics of a random sample of size 3 froma distribution…

A: Given that Z1=Y1Y2Z2=Y2Y3Z3=Y3 Then, Y3=Z3Y2=Z2Z3Y1=Z1Z2Z3

Q: Let X1, X2, ..., Xn be a random sample from the distribution with the pdf f(x; theta) =…

A: From the given information, the probability density function of X is The likelihood function is…

Q: 3.

A: 3. From the given information, the random variable X follows uniform [0,1]. The probability density…

Q: Given that Y1, Y2, Y3, ..., Yn is a random sample from a gamma distribution with parameters alfa =…

A: Given that Y1, Y2,…Yn is a random sample from a two parameter gamma distribution with parameters α=3…

Q: A continuous random variable Z has range equal to the entire real line with pdf fz(2) =e=/2. Find…

A: We have given that a continuous random variable Z has range equal to the entire real line with pdf,…

Q: The joint PDF of two jointly continuous random variables X and Y is c(x² + y?) for 0 < x <1 and 0 <…

A: We have given that, X and Y two continuous random variables having joint PDF is,

Q: Let Y1, Y2,...,Y, denotes a random sample from the uniform distribution on the interval (0,0 + 1).…

A: Given :Let Y1,Y2,..,Yn denotes a random sample from the uniform distributionon the interval…

Q: 2. In the construction of multivariate hypergeometric distribution, show that Y1,...,Yn are п…

A: The Multitype Model As in the basic sampling model, we start with a finite population D consisting…

Q: If X has a uniform distribution U(0, 1), find the pdf of Y = ex with ndf

Q: The PDF of random variable x is given as, 0.3507 Jx, 0<x<3 1,(x): 0, otherwise Find the, Mean

Q: Suppose X and Y are independent, Cauchy random variables with PDFS specified by fx(x) 1/n and fy(y)…

A: From the given information, f(X)=1π(1+x2)f(y)=1π(1+y2) X and Y are independent. Consider, the joint…

Q: Let X, denote the mean of a random sample of size n from a Gamma(, 1) distribution. Show that Vn (X,…

Q: Given the CDF Fy(9) of random variable Y 1 0.8 0.6 0.4 0.2 0 1 2 3 4 5 y Is Y discrete or…

A: Solution

Q: Suppose the random variables X and Y have a joint pdf Sxv(a, y) = { *. x+y 0 VY).

A: Given information: The joint probability density function of the random variables X and Y is as…

Q: Suppose the random variables X and Y have a pdf given by f (x, y) = kæy on 0<x<1,0<y<1 Find k.

A: 4.

Q: Let X have the Poisson distribution with parameter Y, where Y ha he Poisson distribution with…

A: It is given that, Y~PoissonμX|Y~PoissonY We know that if Z~Poissonλ Then, EetZ=eλet-1

Q: Let Y1,..., Yn constitute a random sample from the probability density function given by fy (yl0) =…

A: The probability density function of Y is given below: fYy|θ=2θ2θ-y, for y∈0,θ

Q: Let X1,..., X, be a random sample from a two-parameter Weibull distribution with pdf x > 0 f(x) = 0,…

A: It is an important part of statistics. It is widely used.

Q: Consider a random sample X1,..., Xn with n> 3 from the exponential distribution with parameter > 0…

A: Given that X1,X2,......Xn with n>3 from the exponential distribution with parameter λ>0 and…

Q: Let X and Y be two independent random variables each uniformly distributed over (0, 1). Find the…

A: Continuous uniform distribution: A random variable X is said to have the rectangular distribution or…

Q: Let Y₁, Y2,..., Yn denote a random sample of size n from a population with a uniform distribution on…

Q: Let X be uniformly distributed over (0,4). Calculate E[X5].

A: Given: X follows Uniform distribution over ( 0 , 4)

Q: Let X has Poisson distribution with parameter A such that P(X=2) =9P(X=4) +90P(X=6). Find the value…

A: Solution : Given that, Let , X has poisson distribution with parameter λ such that…

Q: Let X1, X,... An be a random sample from a distribution with pdf f(x.p) = p(1-p)' where 0<p<5 is a…

A: In the given problem sample size n is not given hence I have taken n=19 to find probability of type…

Q: Let Yı, Y2,, Ya be a random sample from the following distribution fG) = {02 for 0sy 202 elsewhere…

A: We want to find the sufficient statistic

Q: be distributed as MVN;(0,1), where 0 = and / = 6 )- Let X = %3D Let the random variables Y, and Y,…

A: The PDF of (X1, X2) is fX1,X2(x1,x2)=12πe-12(x12+x22),(x1,x2)∈R2Let X1=Y1sin Y2 and X2=Y1cos Y2Then,…

Q: Let (X1, ., Xn) be a random sample from the following discrete distribution: 2(1 – 0) P(X1 = 1) =…

Q: Let the random variable Y be defined by Y = BX?,B > 0, where X is a continuous Rayleigh random…

A: The problem can be solved using the concept of pdf and random variables. please find step by step…

Q: Let Y1,...,Yn constitute a random sample from the probability density function given by T(20) fy…

A: Given that fy(θ)=τ(2θ)[τ(θ)]2yθ-1(1-y)θ-1 , for y∈[0,1]

Q: Let X1, X2, X3 be independent Exp()-distributed random vairables. Determine the pdf of X(1)X(3)

A: From the given information,X1, X2, X3 are independent random variable that Exponentially…

Q: Find the pdf for the discrete random variable X whose cdf at the points x =0,1,6 is given by Fx(x)=…

A: The probability density function is known as pdf which contains the interval range where all the…

Q: correlation

A: Given: The joint pdf is f(x,y)=x+y, 0≤x≤1,0≤y≤10, elsewhere

Q: a) Let Y₁, Y2,..., Yn denote a random sample of size n taken from a distribution with probability…

Q: Let (y1, Y2, ..., Yn) be a random sample from the uniform distribution on the interval [A – a/5, 1 +…

Q: with Let Y,, Ke, Ys be ina random Sample from a distribution Pdf fy (gles) = e Le, ) ५) %3D

A: From the given information, fy,θ=e-y-θ, θ<y<∞ Consider, the likelihood function,…

Q: X is nomally distributed with parameters u and o = 20 and that, for a 76. How large of a sample…

A: Given: α≤0.025β≤0.025σ=20μ0=76μ1=82

Q: Let X1,, X, be a random sample from a population with pdf (0 + 1)r", if 0 <r<1 fe(x) = 0, %3D…

A: Given information: Let X1, X2, …, Xn is a random sample of size n taken from a probability…

Q: If X and Y each follow an exponential distribution with parameter 1 and are inde- pendent, find the…

A: Given: X and Y each follow exponential distribution and are independent we want to find pdf of U=X-Y

Q: If X₁, X₂, ..., X is a random sample from the population with E distribution (4,0) with density…

A: 3. From the given information, the density function is, fx|θ=16θ4x3e-xθ, x>0 Consider, the…

Q: Let X be a Laplacian random variable with pdf fx(æ) = ;e-lal, 0 < x < +o. 6. Let Y = a(X), where…

A: Given that f(x)=12e-x,-∞<x<∞ Let Y=g(X) gx=-1, x<-1x, -1≤x≤11,…

Q: Let X and Y be random variables with joint pdf 8xy for 0 fx,y (x, y) where k is a positive…

Q: . Let X1,. , X, be iid data from a uniform distribution over the disc of radius 0 in R?. Thus, X; €…

A: Given X1, X2,...., Xn are samples from uniform distribution over the disc of radius θ in R2 The…

Q: Suppose the distribution of Y, conditional on X, is n(x, x²) and that the marginal distribution of X…

Q: Let X1,…,X, be a random sample from a pdf S(x,0) =: 20? ',x>0,0 > 0

A: From the given information, X1,.....Xn be a random sample from the pdf,

Q: Let X, ...,X, be a random sample with the distribution having pdf f (x; 0,, 02) =e ,0, < <0, -00 <…

A: Maximum likelihood estimation is a method that determines the values for parameters of the…

Q: Fou are given the Posterior pdf fesp[-(8-x)]. e >x = (x\e)c [0. e <x ind (as a function of x) the…

A: It is an important part of statistics. It is widely used.

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Let X, i=1,.,20 be identical independent Poisson RVs distributed with parameter 1 = 2. Calculate and
approximation to P{Ei", ×, > 25}.

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

Assume that the variables Y1, Y2,... in a compound Poisson process have Bernoulli distribution with parameter p . Show that the process reduces to the Poisson process of parameter λp.
Given that Y1, Y2, Y3, ..., Yn is a random sample from a gamma distribution with parameters alfa = 3, and Beta = theta, find the mle of theta.
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).
Let X1, X2, ..., Xn be a random sample from the distribution with the pdf f(x; theta) = theta*x^(theta-1), 0<x<1, 0<theta<infinity, zero elsewhere. Find the mle theta-cap of Theta.
Suppose that the lifetime, X, and brightness, Y, of a light bulb are modeled as continuous random variables. Let their joint pdf be given by:f(x,y)=λ_1λ_2e^{-λ_1x-λ_2y},x,y>0 •Are lifetime and brightness independent?•Are lifetime and brightness uncorrelated?
Let X1, . . . , Xn i.i.d. U([θ1, θ2]), i.e., X1, . . . , Xn are independent and follow a uniform distribution on the interval [θ1, θ2] for θ1, θ2 ∈ R and θ1 < θ2. Find an estimator for θ1 and θ2 using the method of moments.
Let Y1 < Y2 < · · · < Yn be the order statistics of a random sample of size nfrom a distribution with pdf f(x) = 1, 0 < x < 1, zero elsewhere. Show that thekth order statistic Yk has a beta pdf with parameters α = k and β = n − k + 1.
Suppose X, Y, Z are iid observations from a Poisson distribution with parameter λ, which is unknown. Consider the 3 estimators T1 = X + Y − Z, T2 = 2X + Y + Z 4 , T3 = 3X + Y + Z 5 . (a) Which among the above estimators are unbiased? (b) Among the class of unbiased estimators, which has the minimum variance?
Let X1, .... Xn be a random sample from a population with location pdf f(x-Q). Show that the order statistics, T(X1, ...., Xn) = (X(1), ... X(n)) are a sufficient statistics for Q and no further reduction is possible?
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 X1,...,Xn be a random sample from the distribution f(x) = 2x, 0 < x < 1. Find the distribution of the sample maximum X(n)
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?