Question 1b.

Calculate E[I[X=8]].

Exercise 1 [5 points]. This problem reviews basic concepts from probability. a) [1 point]. A biased die has the following probabilities of landing on each face: face 1 2 3 4 5 6 P(face) 1 . 1 .2 .2 .4 0 I win if the die shows even. What is the probability that I win? Is this better or worse than a fair die (i.e., a die with equal probabilities for each face)? b) [1 point]. Recall that the expected value E[X] for a random variable X is E[X] = EP(X = 1) I, TEA where \\' is the set of values X may take on. Similarly, the expected value of any function f of random variable X is ES(X)] = _P(X = x) f(x). TEA Now consider the function below, which we call the "indicator function" 1 if X = a I[X = ] jo ixfa Let X be a random variable which takes on the values 3, 8 or 9 with probabilities pa, ps and po respectively. Calculate E[I [X = 8]]