Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

1)In a certain village, the eldest daughter tends the family’s sheep. Suppose th

ID: 3204829 • Letter: 1

Question

1)In a certain village, the eldest daughter tends the family’s sheep. Suppose that every family in this large village has two children. What proportion of all the daughters are sheep herders? What assumptions did you make?

2) Show that P(A|B) P(A) implies P(A|Bc) P(A), and give an intuitive explanation of why this makes sense

3) Show that if events A1 and A2 have the same probability P(A1) = P(A2), A1 implies B, and A2 implies B, then P(A1|B) = P(A2|B) if it is observed that B occurred. Hint: What does “implies” mean for events/sets?

4) Let X be the outcome of the roll of a fair 6-faced die. Let Y denote independent roll of a fair 6-faced die. the Find the PMF of X + Y and plot its CDF. Make sure you explain how can you use independence to calculate the PMF.

Explanation / Answer

(1) Assumption: The incidence of a boy and a girl are equally likely

The sample space is {BB, BG, GB, GG}

Since the elder daughter tends sheep {GB, GG}, the percentage of daughters who tend sheep is 2/4 = 1/2 or 50%