Question

The random variable X is uniformly distributed in the interval [0, α] for some α >...

The random variable X is uniformly distributed in the interval [0, α] for some α > 0. Parameter α is fixed but unknown. In order to estimate α, a random sample X1, X2, . . . , Xn of independent and identically distributed random variables with the same distribution as X is collected, and the maximum value Y = max{X1, X2, ..., Xn} is considered as an estimator of α.

(a) Derive the cumulative distribution function of Y .



(b) Find the mean and variance of Y , and explain why Y is a good estimator for α when sample size n is large.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

ANSWER:

**Please give me "like".....don't skip....its very important for me now.....

NOTE:: I HOPE YOUR HAPPY WITH MY ANSWER....***PLEASE SUPPORT ME WITH YOUR RATING...

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Included all steps. Thanks The random variable X is uniformly distributed in the interval [0, α]...
Included all steps. Thanks The random variable X is uniformly distributed in the interval [0, α] for some α > 0. Parameter α is fixed but unknown. In order to estimate α, a random sample X1, X2, . . . , Xn of independent and identically distributed random variables with the same distribution as X is collected, and the maximum value Y = max{X1, X2, ..., Xn} is considered as an estimator of α. (a) Derive the cumulative distribution function...
Consider n independent variables, {X1, X2, . . . , Xn} uniformly distributed over the unit...
Consider n independent variables, {X1, X2, . . . , Xn} uniformly distributed over the unit interval, (0, 1). Introduce two new random variables, M = max (X1, X2, . . . , Xn) and N = min (X1, X2, . . . , Xn). (A) Find the joint distribution of a pair (M, N). (B) Derive the CDF and density for M. (C) Derive the CDF and density for N. (D) Find moments of first and second order for...
Let Y1,Y2.....,Yn be independent ,uniformly distributed random variables on the interval[0,θ].，Y(n)=max(Y1,Y2,....,Yn)，which is considered as an estimator...
Let Y1,Y2.....,Yn be independent ,uniformly distributed random variables on the interval[0,θ].，Y(n)=max(Y1,Y2,....,Yn)，which is considered as an estimator of θ. Explain why Y is a good estimator for θ when sample size is large.
You are given that X1 and X2 are two independent and identically distributed random variables with...
You are given that X1 and X2 are two independent and identically distributed random variables with a Poisson distribution with mean 2. Let Y = max{X1, X2}. Find P(Y = 1).
Suppose that X is uniformly distributed on the interval [0,5], Y is uniformly distributed on the...
Suppose that X is uniformly distributed on the interval [0,5], Y is uniformly distributed on the interval [0,5], and Z is uniformly distributed on the interval [0,5] and that they are independent. a)find the expected value of the max(X,Y,Z) b)what is the expected value of the max of n independent random variables that are uniformly distributed on [0,5]? c)find pr[min(X,Y,Z)<3]
Suppose X1, X2, X3, and X4 are independent and identically distributed random variables with mean 10...
Suppose X1, X2, X3, and X4 are independent and identically distributed random variables with mean 10 and variance 16. in addition, Suppose that Y1, Y2, Y3, Y4, and Y5are independent and identically distributed random variables with mean 15 and variance 25. Suppose further that X1, X2, X3, and X4 and Y1, Y2, Y3, Y4, and Y5are independent. Find Cov[bar{X} + bar{Y} + 10, 2bar{X} - bar{Y}], where bar{X} is the sample mean of X1, X2, X3, and X4 and bar{Y}...
A uniform random variable on (0,1), X, has density function f(x) = 1, 0 < x...
A uniform random variable on (0,1), X, has density function f(x) = 1, 0 < x < 1. Let Y = X1 + X2 where X1 and X2 are independent and identically distributed uniform random variables on (0,1). 1) By considering the cumulant generating function of Y , determine the first three cumulants of Y .
6. Let X1, X2, ..., Xn be a random sample of a random variable X from...
6. Let X1, X2, ..., Xn be a random sample of a random variable X from a distribution with density f (x)  ( 1)x 0 ≤ x ≤ 1 where θ > -1. Obtain, a) Method of Moments Estimator (MME) of parameter θ. b) Maximum Likelihood Estimator (MLE) of parameter θ. c) A random sample of size 5 yields data x1 = 0.92, x2 = 0.7, x3 = 0.65, x4 = 0.4 and x5 = 0.75. Compute ML Estimate...
Suppose that X1,..., Xn form a random sample from the uniform distribution on the interval [0,θ],...
Suppose that X1,..., Xn form a random sample from the uniform distribution on the interval [0,θ], where the value of the parameter θ is unknown (θ>0). (1)What is the maximum likelihood estimator of θ? (2)Is this estimator unbiased? (Indeed, show that it underestimates the parameter.)
f X1,X2,X3,X,X5 are independent and identically distributed geometrically distributed ran dom variables with the parameter p,...
f X1,X2,X3,X,X5 are independent and identically distributed geometrically distributed ran dom variables with the parameter p, compute (a) Find c.d.f. of Ymax = max{X1,...,X5}; (b) Find p.d.f. of Ymin = min{X1,...,X5}
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT