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1. Let’s assume you want to research prisoner abuse. You need a way to measure prisoner...

1. Let’s assume you want to research prisoner abuse. You need a way to measure prisoner abuse so that when you gather data you can record the level of abuse. You could just have a dichotomous variable that indicates if abuse happened or not. What is the mean of such variable? (0.5 point)
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Answer #1

Suppose our dichotomous variable is X and it is a nominal variable which has 2 categories - abuse happened, abuse did not happen. Since we have two outcomes, we can define our variable like this:
X = 1, if "abuse happened" with probability 'p'.
= 0, if "abuse did not happen" with probability '1 - p'.

This is like a Bernoulli variable and the mean of X will be = p = E(X). If we consider p = 1/2, then E(X) = p = 0.5 = mean of the variable.

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