What is the distribution of theta given these observations

Reference no: EM13607193

In a jury, there are 12 selected jurors. We are looking to see how many prospective people should go to jury duty. Suppose whenever a pool of n prospective jurors is called into voir dire, the number of rejected jurors is X, where X|theta is B(n,theta). Suppose also that historically, the proportion of rejected jurors has fluctuated in the 30%-60% range, inspiring the assignment of the Uniform (.3,.6) prior on theta. Suppose also that two recent school-system cases are randomly selected from among all school system cases and that in the first case, 21 out of 27 prospective jurors were unable to serve, and in the second case, 30 out of 40 were unable to serve.

a. What is the distribution of theta given these observations?

b. What is the mean of the prior distribution? To 4 decimals, what is the mean of the posterior distribution? Why does the relationship between these two numbers make qualitative sense?

c. What is the conditional probability that 1 randomly selected prospective juror will be unable to serve?

d. What is the unconditional probability that of 5 randomly selected prospective jurors, 3 will be unable to serve?

e. What are the name and parameters of the posterior distribution of theta if the prior had been Uniform {0,1}?

Reference no: EM13607193

Questions Cloud

Well-established and well-funded software company began : during january 2010 sophisticated software inc. ssi a well-established and well-funded software company began

Let x1 x2 x3nbspbe three independent random variables with : let x1 x2 x3nbspbe three independent random variables with binomial distributionsb4 12 b6 13 b12

On september 1 howe office supply had an inventory of 30 : on september 1 howe office supply had an inventory of 30 pocket calculators at a cost of 18 each. the company uses a

What was the students average velocity during his trip take : a student wanted to drive from austin to san antonio 80 miles south of austin on highway i35. unfortunately he entered

What is the distribution of theta given these observations : in a jury there are 12 selected jurors. we are looking to see how many prospective people should go to jury duty.

On january 1 2007 the queen corporation issued 8 bonds with : on january 1 2007 the queen corporation issued 8 bonds with a face value of 95000. the bonds are sold for 92150. the

Radioactive decay of granite and other rocks in earths : radioactive decay of granite and other rocks in earths interior provides sufficient energy to keep the interior molten

Rocky mountain chocolates rmc experiences much greater : rocky mountain chocolates rmc experiences much greater demand during the holidays than during the remainder of the

Presented is information related to rogers co for the month : presented is information related to rogers co. for the month of january 2010. ending inventory per perpetual records

User Account

All Pages