# Question: Find a sufficient statistic for given a random sample

Find a sufficient statistic for θ, given a random sample, X1, X2, . . . , Xn, from a distribution with pdf

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

Let X1, X2, . . . , Xn be a random sample from N(0, σ2), where n is odd. Let Y and Z be the mean and median of the sample. Argue that Y and Z − Y are independent so that the variance of Z is Var(Y) + Var(Z− Y). We know ...Let X1, X2, . . . , Xn be a random sample from a gamma distribution with known α and with θ = 1/τ. Say τ has a prior pdf that is gamma with parameters α0 and θ0, so that the prior mean is α0θ0. (a) Find the posterior ...A leakage test was conducted to determine the effectiveness of a seal designed to keep the inside of a plug airtight. An air needle was inserted into the plug, and the plug and needle were placed under water. The pressure ...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 ...Let p equal the proportion of letters mailed in the Netherlands that are delivered the next day. Suppose that y = 142 out of a random sample of n = 200 letters were delivered the day after they were mailed. (a) Give a point ...Post your question