# Question: For determining half lives of radioactive isotopes it is important to

For determining half-lives of radioactive isotopes, it is important to know what the background radiation is in a given detector over a specific period. The following data were taken in a γ-ray detection experiment over 98 ten-second intervals:

Assume that these data are observations of a Poisson random variable with mean λ.

(a) Find the values of and s2.

(b) What is the value of the maximum likelihood estimator of λ?

(c) Is S2 an unbiased estimator of λ?

(d) Which of and s2 would you recommend for estimating λ? Why? You could compare the variance of with the variance of S2, which is

Assume that these data are observations of a Poisson random variable with mean λ.

(a) Find the values of and s2.

(b) What is the value of the maximum likelihood estimator of λ?

(c) Is S2 an unbiased estimator of λ?

(d) Which of and s2 would you recommend for estimating λ? Why? You could compare the variance of with the variance of S2, which is

**View Solution:**## Answer to relevant Questions

Let (a) Show that the maximum likelihood estimator of θ is The data in the following table, part of a set of data collected by Ledolter and Hogg, provide the number of miles per gallon (mpg) for city and highway driving of 2007 midsize-model cars, as well as the curb weight of the ...Let X1, X2, . . . , Xn be a random sample from a gamma distribution with known parameter α and unknown parameter θ > 0 (b) Show that the maximum likelihood estimator of θ is a function of Y and is an unbiased estimator of ...Let X1, X2 be a random sample from the Cauchy distribution with pdf Consider the non-informative prior h(θ1, θ2) ∝ 1 on that support. Obtain the posterior pdf (except for constants) of θ1, θ2 if x1 = 3 and x2 = 7. For ...Twenty-four 9th- and 10th-grade high school girls were put on an ultra-heavy rope-jumping program. The following data give the time difference for each girl (“before program time” minus “after program time”) for the ...Post your question