Question

X be random variable with distribution negative binomial NB(p,r) . r is known, 0<p<1 unknown. Find...

X be random variable with distribution negative binomial NB(p,r) . r is known, 0<p<1 unknown. Find the UMVUE of log (p)

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

Homework Answers

Answer #1

X be random variable with distribution negative binomial NB(p,r) . r is known, 0<p<1 unknown. The pmf is

We know that X is sufficient and complete for p. Let us assume the UMVUE of log(p) is g(X) where g fucntion statisfing E(g(X))= log(p). Then

Hence g(r) =0 and

This is the UMVUE of log(p).

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
X is a binomial random variable with n = 15 and p = 0.4. a. Find...
X is a binomial random variable with n = 15 and p = 0.4. a. Find using the binomial distribution. b. Find using the normal approximation to the binomial distribution.
If random variable X has a binomial distribution with n =8 and P(success) = p =0.5,...
If random variable X has a binomial distribution with n =8 and P(success) = p =0.5, find the probability that X is at most 3. (That is, find P(X ≤ 3))
Suppose that a random variable X has a binomial distribution with n=2, p=0.5. Find the mean...
Suppose that a random variable X has a binomial distribution with n=2, p=0.5. Find the mean and variance of Y = X2
The random variable X has a Binomial distribution with parameters n = 9 and p =...
The random variable X has a Binomial distribution with parameters n = 9 and p = 0.7 Find these probabilities: (see Excel worksheet) Round your answers to the nearest hundredth P(X < 5) P(X = 5) P(X > 5)
True or False? 19. In a binomial distribution the random variable X is discrete. 20. The...
True or False? 19. In a binomial distribution the random variable X is discrete. 20. The standard deviation and mean are the same for the standard normal distribution. 21. In a statistical study, the random variable X = 1, if the house is colonial and X = 0 if the house is not colonial, then it can be stated that the random variable is continuous. 22. For a continuous distribution, P(X ≤ 10) is the same as P(X<10). 23. For...
Suppose X is binomial random variable with n = 18 and p = 0.5. Since np...
Suppose X is binomial random variable with n = 18 and p = 0.5. Since np ≥ 5 and n(1−p) ≥ 5, please use binomial distribution to find the exact probabilities and their normal approximations. In case you don’t remember the formula, for a binomial random variable X ∼ Binomial(n, p), P(X = x) = n! x!(n−x)!p x (1 − p) n−x . (a) P(X = 14). (b) P(X ≥ 1).
x is a binomial random variable with n=10 and p=.5. find the probability of obtaining from...
x is a binomial random variable with n=10 and p=.5. find the probability of obtaining from 6 to 9 tails of a fair coin. use the binomial probability distribution formula
Consider a random variable X with the following probability distribution: P(X=0) = 0.08, P(X=1) = 0.22,...
Consider a random variable X with the following probability distribution: P(X=0) = 0.08, P(X=1) = 0.22, P(X=2) = 0.25, P(X=3) = 0.25, P(X=4) = 0.15, P(X=5) = 0.05 Find the expected value of X and the standard deviation of X.
Let X be a binomial random variable with n = 8, p = 0.4. Find the...
Let X be a binomial random variable with n = 8, p = 0.4. Find the following values. (Round your answers to three decimal places.) (a)     P(X = 4) (b)     P(X ≤ 1) (c)     P(X > 1)
A random variable XX with distribution Exponential(λ)Exponential(λ) has the memory-less property, i.e., P(X>r+t|X>r)=P(X>t) for all r≥0...
A random variable XX with distribution Exponential(λ)Exponential(λ) has the memory-less property, i.e., P(X>r+t|X>r)=P(X>t) for all r≥0 and t≥0.P(X>r+t|X>r)=P(X>t) for all r≥0 and t≥0. A postal clerk spends with his or her customer has an exponential distribution with a mean of 3 min3 min. Suppose a customer has spent 2.5 min2.5 min with a postal clerk. What is the probability that he or she will spend at least an additional 2 min2 min with the postal clerk?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT