NCC Two Dice Conditional Expectation Calculation Worksheet
Description
1) Two dice conditional expectation calculation: Consider the experiment of rolling two honest dice (with the usual sample space). Let X be the random variable that gives the sum of the two numbers rolled, let Y be the random variable that gives the absolute value of the difference of the two numbers rolled (so its value would be 2 for both (5,3) and (2,4) for example), and let Z be the minimum of the two numbers rolled.
- List the range of values possible for each of the random variables X, Y, and Z.
- Compute E(X), E(Y), and E(Z).
- Determine the distribution of E[X|Z] and E[Z|X].
- Compute E[E[X|Z]] and E[E[Z|X]].
- Based on the calculations in (d), what do you expect the value of E[E[Y|X]] and E[E[X|Y]] to be?
2) Is E[X|Y] a number or a random variable?
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