US STAST. 6.For a sample of dental claims x,, X,, ..., X10, you are given:(i)Ex, = 3860 and x = 4,574,802(ii)Claims are assumed to follow a lognormal distribution with parameters u and o .(iii)u and o are estimated using the method of moments.Calculate E[X^ 500] for the fitted distribution.

Answered: Image /qna-images/answer/26212940-8429-4b39-8560-41e1c2ae24c3.jpg

Answered: For a sample of dental claims x, X2,…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Suppose X1, . . . , Xn ∼ Exponential(λ) is a set of n observations drawn independently from an Exponential distribution. (e) Take the second partial derivative of the score function. (f) Check to make sure this value is negative to ensure that the log-likelihood function is concave down.
The following data consists of the times to relapse and the times to death following relapse of 10 bone marrow transplant patients. In the sample patients 4 and 6 were alive in relapse at the end of the study and patients 7–10 were alive, free of relapse at the end of the study. Suppose the time to relapse had an exponential distribution with hazard rate lambda and the time to death in relapse had a Weibull distribution with parameters theta and alpha (a) Construct the likelihood for the relapse rate lambda. (c) Suppose we were only allowed to observe a patients death time if the patient relapsed. Construct the likelihood for theta and alpha based on this truncated sample
Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample?
Suppose that Y has an exponential distribution with mean Beta. Show that 2Y/Beta has a chi square distribution with 2 degrees of freedom.
Suppose that X has a lognormal distribution with parameters θ = 5 and ω2 = 9. Determine the following: a. P(X < 13,300)b. Value for x such that P(X ≤ x) = 0.95c. Mean and variance of X
2) The time between successive customers coming to the market is assumed to have Exponential distribution with parameter l. a) If X1, X2, . . . , Xn are the times, in minutes, between successive customers selected randomly, estimate the parameter of the distribution. b) b) The randomly selected 12 times between successive customers are found as 1.8, 1.2, 0.8, 1.4, 1.2, 0.9, 0.6, 1.2, 1.2, 0.8, 1.5, and 0.6 mins. Estimate the mean time between successive customers, and write down the distribution function. c) In order to estimate the distribution parameter with 0.3 error and 4% risk, find the minimum sample size.
In the daily production of a certain kind of rope, the number of defects per foot given by Y is assumed to have a Poisson distribution with mean ? = 4. The profit per foot when the rope is sold is given by X, where X = 70 − 3Y − Y2. Find the expected profit per foot.
Show that a gamma distribution with α > 1 has a rel-ative maximum at x = β(α − 1). What happens when 0 <α< 1 and when α = 1?
Let X1 and X2 be IID exponential with parameter > 0. Determine the distribution ofY = X1=(X1 + X2).
Suppose the distribution of the time $X$ (in hours) spent by students at a certain university on a particular project is gamma with parameters $\alpha=50$ and $\beta=2 .$ Because $\alpha$ is large, it can be shown that $X$ has approximately a normal distribution. Use this fact to compute the approximate probability that a randomly selected student spends at most 125 hours on the project.
a. What is the probability that the lifetime X of the first component exceeds 3? b. What are the marginal pdf's of X and Y? Are the two lifetimes independent? x. What is the probability that the lifetime of at least one component exceeds 3?
The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 1000 cfs (cubic feet per second). b) What water-pumping capacity should the station maintain during early afternoons so that the probability that demand will be below the capacity on a randomly selected day is 0.995? c) Of the three randomly selected afternoons, what is the probability that on at least two afternoons the demand will exceed 700 cfs?

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS

For a sample of dental claims x, X2, ..., X0 • you are given: (i) Ex, = 3860 and E = 4,574,802 %3D (ii) Claims are assumed to follow a lognormal distribution with parameters µ and o . (iii) u and o are estimated using the method of moments. Calculate E[ X ^ 500] for the fitted distribution.