Question

Let Y1 < Y2 < Y3 < Y4 be the order statistics of a random sample...

Let Y1 < Y2 < Y3 < Y4 be the order statistics of a random sample of size n = 5 (Y1 < Y2 < Y3 < Y4 <Y5). from the distribution having pdf f(x) = e−x, 0 < x < ∞, zero elsewhere. Find P(Y5 ≥ 3).

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

Homework Answers

Answer #1

is the order statistics of a random sample of size n=5 from the distribution having pdf

, where the random sample is , n=5

Since if maximum of the sample is less than 3, implies each sample observation is less than 3.

, since, a random sample is always independently and identically distributed.

So,

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
Let Y1, Y2, Y3 ,..,, Yn be a random sample from a normal distribution with mean...
Let Y1, Y2, Y3 ,..,, Yn be a random sample from a normal distribution with mean µ and standard deviation 1. Then find the MVUE( Minimum - Variance Unbiased Estimation) for the parameters: µ^2 and µ(µ+1)
Problem 3. Let Y1, Y2, and Y3 be independent, identically distributed random variables from a population...
Problem 3. Let Y1, Y2, and Y3 be independent, identically distributed random variables from a population with mean µ = 12 and variance σ 2 = 192. Let Y¯ = 1/3 (Y1 + Y2 + Y3) denote the average of these three random variables. A. What is the expected value of Y¯, i.e., E(Y¯ ) =? Is Y¯ an unbiased estimator of µ? B. What is the variance of Y¯, i.e, V ar(Y¯ ) =? C. Consider a different estimator...
Let Y1, Y2, . . ., Yn be a random sample from a Laplace distribution with...
Let Y1, Y2, . . ., Yn be a random sample from a Laplace distribution with density function f(y|θ) = (1/2θ)e-|y|/θ for -∞ < y < ∞ where θ > 0. The first two moments of the distribution are E(Y) = 0 and E(Y2) = 2θ2. a) Find the likelihood function of the sample. b) What is a sufficient statistic for θ? c) Find the maximum likelihood estimator of θ. d) Find the maximum likelihood estimator of the standard deviation...
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}...
Let Y1, Y2, …, Yndenote a random sample of size n from a population whose density...
Let Y1, Y2, …, Yndenote a random sample of size n from a population whose density is given by f(y) = 5y^4/theta^5 0<y<theta 0 otherwise a) Is an unbiased estimator of θ? b) Find the MSE of Y bar c) Find a function of that is an unbiased estimator of θ.
1. Let Y1 < Y2 < · · · Ym be the order statistics of m...
1. Let Y1 < Y2 < · · · Ym be the order statistics of m independent observations X1, · · · , Xm from a uniform distribution on the interval [θ, θ + 1]. (a) (5 points) Find the distribution of Yr, where r is a integer and 1 ≤ r ≤ m. (b) (5 points) Calculate V ar(Ym) if θ = 0. (c) (5 points) Suppose θ is unknown, m = 5 and we have observed that x1...
Let Y1,Y2,...,Yn denote a random sample of size n from a population with a uniform distribution...
Let Y1,Y2,...,Yn denote a random sample of size n from a population with a uniform distribution on the interval (0,θ). Let Y(n)= max(Y1,Y2,...,Yn) and U = (1/θ)Y(n) . a) Show that U has cumulative density function 0 ,u<0, Fu (u) =   un ,0≤u≤1, 1 ,u>1
Let Y1,Y2,Y3,...,Yn denote a random sample from a Poisson probability distribution. (a) Show that sample mean,...
Let Y1,Y2,Y3,...,Yn denote a random sample from a Poisson probability distribution. (a) Show that sample mean, ˆ θ1 = ¯ Y and the sample variance, ˆ θ2 = S2 are both unbiased estimators of θ. (b) Calculate relative efficiency of the two estimators in (a). Based on your calculation, Which of the two estimators in 3a would you select as a better estimator?
Let Y1, Y2, . . . , Yn denote a random sample from a uniform distribution...
Let Y1, Y2, . . . , Yn denote a random sample from a uniform distribution on the interval (0, θ). (a) (5 points)Find the MOM for θ. (b) (5 points)Find the MLE for θ.
Let y1,y2,...,yn denote a random sample from a Weibull distribution with parameters m=3 and unknown alpha:...
Let y1,y2,...,yn denote a random sample from a Weibull distribution with parameters m=3 and unknown alpha: f(y)=(3/alpha)*y^2*e^(-y^3/alpha) y>0 0 otherwise Find the MLE of alpha. Check when its a maximum
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT