Question

A random variable X with a beta distribution takes on values between 0 and 1, with...

A random variable X with a beta distribution takes on values between 0 and 1, with unknown α and β.

a) Use the method of moments to obtain an estimator forαandβ.

b) Are the estimators sufficient statistics?

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

Homework Answers

Answer #1

a)

b)

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 X be a random variable that takes on values between 0 and c. That is...
Let X be a random variable that takes on values between 0 and c. That is P{0 ≤ X ≤ c} = 1. Show that V ar(X) ≤ c2 4 Hint: One approach is to first argue that E[X2] < cE[X] and then use this fact to show that V ar(X) ≤ c2[α(1 − α)] where α = E[X]/c.
Let X1, X2, . . . Xn be iid random variables from a gamma distribution with...
Let X1, X2, . . . Xn be iid random variables from a gamma distribution with unknown α and unknown β. Find the method of moments estimators for α and β
If a random variable X has a beta distribution, its probability density function is fX (x)...
If a random variable X has a beta distribution, its probability density function is fX (x) = 1 xα−1(1 − x)β−1 B(α,β) for x between 0 and 1 inclusive. The pdf is zero outside of [0,1]. The B() in the denominator is the beta function, given by beta(a,b) in R. Write your own version of dbeta() using the beta pdf formula given above. Call your function mydbeta(). Your function can be simpler than dbeta(): use only three arguments (x, shape1,...
Let B > 0 and let X1 , X2 , … , Xn be a random...
Let B > 0 and let X1 , X2 , … , Xn be a random sample from the distribution with probability density function. f( x ; B ) = β/ (1 +x)^ (B+1), x > 0, zero otherwise. (i) Obtain the maximum likelihood estimator for B, β ˆ . (ii) Suppose n = 5, and x 1 = 0.3, x 2 = 0.4, x 3 = 1.0, x 4 = 2.0, x 5 = 4.0. Obtain the maximum likelihood...
5. Consider the random variable X with the following distribution function for a > 0, β...
5. Consider the random variable X with the following distribution function for a > 0, β > 0: FX (z) = 0 for z ≤ 0 ​= 1 – exp [–(z/a)β] for z > 0 (where exp y = ey) (a) Determine the inverse function of FX (z), where 0 < z < 1. (b) Let a = β = 2 for the random variable X, and define the numbers u1 = .33 and u2 = .9. Use the inverse...
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 the random variable X has pdf f(x;?, ?)=??x?−1e−?x? for x≥0;?, ? > 0. a) Find...
Suppose the random variable X has pdf f(x;?, ?)=??x?−1e−?x? for x≥0;?, ? > 0. a) Find the maximum likelihood estimator for ?, assuming that ? is known. b) Suppose ? and ? are both unknown. Write down the equations that would be solved simultaneously to find the maximum likelihood estimators of ? and ?.
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)...
A Poisson random variable is a variable X that takes on the integer values 0 ,...
A Poisson random variable is a variable X that takes on the integer values 0 , 1 , 2 , … with a probability mass function given by p ( i ) = P { X = i } = e − λ λ i i ! for i = 0 , 1 , 2 … , where the parameter λ > 0 . A)Show that ∑ i p ( i ) = 1. B) Show that the Poisson random...
Let X be a discrete random variable that takes on the values −1, 0, and 1....
Let X be a discrete random variable that takes on the values −1, 0, and 1. If E (X) = 1/2 and Var(X) = 7/16, what is the probability mass function of X?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT