4)Let X₁, X₂,..., Xn be mutually independent and identically distributed continuousrandom variables with the following density function,f(x) = {630x*(1-x)¹ for 0 < x < 10,otherwisea)Use the Chebychev inequality to find the value of k, for P(0.2 ≤ x ≤ 0.8).b) What is the upper and lower bound of P(0.2 < X < 0.8)?c) Use the central limit theorem to find P(9.5 ≤X ≤ 10.5).

From the given information, fx=630x41-x4, for 0<x<1 Consider, μ=∫01xfxdx =∫01x*630x41-x4dx…

Answered: 4) Let X₁, X₂,..., Xn be mutually…

4) Let X₁, X₂,..., Xn be mutually independent and identically distributed continu random variables with the following density function, for 0

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: Let X and Y be independent random variables with density ƒ (æ) = 3x² for 0 < x < 1. Then P (X + Y <…

A: Given Information: Let X and Y be independent random variables with the pdf: fx=3x2 ,…

Q: Let the joint density of random variables x and y be given by the following: fx,y(x,y) = 0.158(x +…

A: As per the guidelines, solving first question when multiple questions are posted. Kindly re-post the…

Q: Let X be a continuous random variable with PDF fx(x) = { 5x4 0<x< 1 otherwise If Y = 1/X², calculate…

A: The is a continuous random variable. The PDF is, Here, The objective is to find .

Q: Let X1, X2, X, is a random sample from a distribution with density function 302e-³ for 0<x<x f(x; 0)…

Q: If X is a random variable with probability density function 32 f (x) = for x = 0, 1, 2, 3, 4 and 5,…

A: Formula : Variance :

Q: Let X and Y be independent and identical exponential random variables with parameter 0. Showthat Z =…

A: and represent independent and identical exponential random variables.The parameterIt must be shown…

Q: An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and…

A: From the information, given thatLet Factor A denotes the method of loading and unloadingLet Factor B…

Q: Let X and Y be two continuous random variables having joint pdf fX,Y (x, y) = (1 + XY)/4 , −1 ≤x ≤1,…

A: Given that, X and Y are two continuous random variables. The joint pdf of X and Y is given as:…

Q: X is a uniform random variable over the interval (3, 5). Find the density function of X for the…

A: Solution: From the given information, X follows uniform distribution with parameters a=3 and b=5.

Q: Let X1,, X, denote a random sample of size n from the population with probability density function…

Q: ) Write the joint probability density function. p) Express F(z) = P(¥ <z) using integrals and…

A: Let X and Y be continuous independent random variable have exponential distribution with mean θ

Q: Let X1,..., Xn be a random sample from a population with probability density function (pdf) f(x | 0)…

A: We have given that Let X 1 ,...,X n be a random sample from a population with probability density…

Q: Let X be a continuous random variable with density f (x) = 24x-4 for æ > 2. Then Var (X) is equal to

Q: For the random variable X with the density function f(x) = {2/ compute Var(X): ☐ and sd(X): 2/x2 for…

A: Step 1: The probability density function of the random variable X is, Step 2: The variance of X is,…

Q: Let f(x) is density function of continuous random variable x then the (expected value E(x E&) = […

A: Given that, X is a continuous random variable, and f(x) be the p.d.f. of X.

Q: Let X1, X2, and X3 be independent random variables from (-1, 1). Find the probability density…

A: Probability Density Function: Probability is deals with the random…

Q: Let X,, X2,.. ,X, be a random sample from a distribution with density function if x 20 -e f(x; 0)…

A: The answer is given using the concept of maximum likelihood. please find step by step solution…

Q: Let X1, X2,..., X, is a random sample from a distribution with density function f(x; 0) = 302e-0³…

A: The given probability density function (PDF) is:f(x;θ)=302e^-θ3for0x∞,otherwise

Q: Suppose that random variables X₁ and X₂ have exponential distribution with expecteu value of and…

A: Solution

Q: Let X be a continuous random variable with PDFfx(x)= 8/x3, x> 2. Find E[W where W = X/3.

Q: (b) The expression for the joint probability density function of the transformed random variables U…

Q: Let X1,., X, denote a random sample from the probability density function f(r) = 0x-1, 0 0. Show…

Q: For a random variable (X) having pdf given by: f(x) = (k)x^3 where 0 ≤ x ≤ 1, compute the following:…

A: Given,f(x)=kx3 ; 0≤x≤1

Q: Find the density of Z = (X+ Y)2, where X and Y are independent uniform random variables over (-1,…

Q: Q4. Consider the following data (16, 7, 5, 16, 17, 17, 18, 20, 19, 20, 18, 32, 31, 30), how many…

A: Outliers: Any values in the data set below Q1-1.5×IQR and above Q3+1.5×IQR are considered as…

Q: 4. Let X₁ and X₂ be independent identically distributed random variables both having exponential…

A: Let X1 and X2 be independent and identically distributed random variables both having an exponential…

Q: b) Let X₁, X₂, X, denote a random sample of size n from a distribution with probability density…

A: f(x; θ)=θ(1-x)-(1+θ) x>0

Q: Let X and Y are two random variables with p.d.f as F(x,y) = 3x^2y+3xy^2,0 < x< 1,0 < y < 1. (i) Find…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Let X₁, X₂, X3.....X₁ be a random sample of n from population X distributed with the fol probability…

A: Solution is given below

Q: b) Let X₁, X2, X3,...,Xn be a random sample of n from population X distributed with the following…

A: As per the Bartleby guildlines we have to solve first three subparts and rest can be reposted....…

Question

4)
Let X₁, X₂,..., Xn be mutually independent and identically distributed continuous
random variables with the following density function,
f(x) = {630x*(1-x)¹ for 0 < x < 1
0,
otherwise
a)
Use the Chebychev inequality to find the value of k, for P(0.2 ≤ x ≤ 0.8).
b) What is the upper and lower bound of P(0.2 < X < 0.8)?
c) Use the central limit theorem to find P(9.5 ≤X ≤ 10.5).

Expert Solution

Step 1

From the given information,

$f (x) = 630 x^{4} {(1 - x)}^{4}, f o r 0 < x < 1$

Consider,

$μ = \int_{0}^{1} x f (x) d x = \int_{0}^{1} x * 630 x^{4} {(1 - x)}^{4} d x = \int_{0}^{1} 630 x^{5} {(1 - x)}^{4} d x = 0.5$

$σ^{2} = \int_{0}^{1} x^{2} f (x) d x - μ^{2} = \int_{0}^{1} 630 x^{6} {(1 - x)}^{4} d x - 0 . 5^{2} = 0.2727 - 0.25 = 0.023$

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

The density function, ху fy(x, y) = f(x) =9 0, 0
a) Let X be a continuous random variable with the following probability density function (2x3 f(x)={11 2 +5) , 0
Let X₁, X2, X3,..., Xn denote a random sample of size n from the population distributed with the following probability density function: I e) f) g) where k> 0 is a constant. f(x; 2) = 2-kxk-1e (k-1)! if x > 0 elsewhere " Justify whether or not Â is a uniform minimum variance unbiased estimator of 1. Check whether or not the MLE of λ is a consistent. Suggest with a Fisher's factorization theorem, the sufficient estimator of 1.
b) Let X₁, X2, X3.....Xn be a random sample of n from population X distributed with the following probability density function: ze zo, f(x;0)=√2m0 0, (i) Find the parameter space of 0. (ii) Find the maximum likelihood estimator of 0. if -∞
Let X1,...,X, be independent random variables with pdfs -{* 0 -i(0 – 1) 0. Find a two-dimensional sufficient statistic for 0.
I need #4 answered
Suppose that X and Y are statistically independent and identically distributed uniform random variables on (0,1). (a) Write down the joint probability density function fx,y(x,y) of X and Y on its support.
Let Y₁, Y₂,..., Yn be a random sample from the inverse Gaussian distribution with probability density function: f(y, μ, 2) = { Where μ and are unknown. a) What are i. 1 -ACT √ λ 2ny3)že elsewhere if y > 0 the likelihood ii. the log likelihood functions of u and λ. b) Find the maximum likelihood estimators of u and 2.
Asap