Three balanced coins are tossed independently. One of the variables of interest is Y1, the number of heads. Let Y2 denote the amount of money won on a side bet in the following manner. If the first head occurs on the first toss, you win $1. If the first head occurs on toss 2 or on toss 3 you win $2 or $3, respectively. If no heads appear, you lose $1 (that is, win $1). a Find the joint probability function for Y1 and Y2. b What is the probability that fewer than three heads will occur and you will win $1 or less? [That is, find F(2, 1).]

Week 7: Probability Distributions 18 October 2016 Basic Statistics for Research Professor HK Dong Wendy Liu Baye’s Rule – given k mutually exclusive & exhaustive events such that and an observed event A, then Permits revising old probabilities based on new info o Prior probability – associated w/ B andbefore we know status of A and...