Question 1

You realize your wallet is missing. You have either left in the office or at a friends' place. It seems very likely, say80%

likely, that your friend would have texted you by now if you had left it at her place. You know it is unlikely, (say5%

probability), that someone in the office would have tracked you down by now if you had lost it there. You have not been contacted.

What other information do you need in order compute the probability that you left it in the office?

SELECT ALL THAT APPLY and select none of the above if none of the choices can be

a)used to compute the proabbility that you left it in the office.

b)the conditional probability that you left it at your friends.

c)the conditional probability that you left it in the office.

d)the prior probability that you left your wallet in the office.

e)None of the above.

Question 2

Consider aB(n,p)

and aH(A,B,n)

wherep=A/(A+B).

Which of the following statements is true? SELECT ALL THAT APPLY

a)The variance of the binomial is always smaller than the variance of the hypergeometric.

b)The variance of the hypergeometric is always smaller than or equal to the variance of the binomial.

c)The relative sizes of the variances depend on the choice ofn

andp.

d)The variance of the binomial is always smaller than or equal to the variance of the hypergeometric.

Question 3

The Poisson distribution is a special case of the exponential distribution.

True or False?

Question 4

Knowing the distribution of the test statistic under the null allows you to calculate(the probability of a type I error) and(the probability of a type II error).

True or False?

Question 5

Suppose that judges can decide to whom they give a GPS bracelet to when individuals who have been arrested for a crime are released on bail (pending judgement).

Separately, a researcher runs an RCT for the impact of bracelets: people who are released on bail are randomly assigned to recieve a bracelet or not. She finds that the bracelet reduces the probability of committing a crime while on bail by 5 percentage points (and this difference is significant).

Another researcher obtains a separate data set on the regular program (where the judge can decide whether or not to give the bracelet), that has many variables about the people who were arrested (including whether or not they were given a bracelet when released), and runs a machine learning algorithm to find out what predicts whether someone will commit a crime while on bail.They find that the bracelet tends to predict greater recidivism (recidivism means relapse into criminal behavior)

This implies that one of the two studies must be incorrect.

True or False?