Question

QUESTION 1

1. Imagine you just had an election between two candidates: Abby and Tanya. There are 10,000 voters. After you count each vote, you calculate the percent of the vote Abby has so far. (In other words, you record the percent of counted voters who voted for Abby after one vote is counted, then after a second vote is counted, then after a third vote is counted, etc.)

   If you graphed Abby's percent of support after each vote counted, with the number of votes counted on the x-axis, how should the graph look? (Keep in mind the law of large numbers.)

   		Volatile on the left and smoothly upward or downward sloping (depending on if she wins or loses) on the right.
   		Smoothly upward or downward sloping (depending on if she wins or loses) on the left and volatile on the right.
   		Volatile on the left and flat on the right.
   		Flat on the left and volatile on the right.

20 points   

QUESTION 2

1. Randy and Monica have three sons. They love their sons but they would like to have a daughter. Randy convinces Monica to have a fourth child because, according to the law of large numbers, the child is likely to be female. Is Randy correct?

   		No, because Randy’s succumbing to the gambler’s fallacy.
   		No, because Randy’s succumbing to the hot hand fallacy.
   		Yes, because as the number of trials increases the empirical average should approach the theoretical average.
   		No, because they are more likely to have a so

Answer 1

a)

Law of large numbers states that if you repeat an experiment independently a large number of times and average the result, what you obtain should be close to the expected value.

During counting of votes, at first the numbers might be fluctuate or all over the graph as numbers are low at the starting.

But as the Law of Large Numbers will take start to take effect, the final results of counting will give the clear picture.

If the candidate is winning then it will move upward else downward.

Answer: Volatile on the left and smoothly upward or downward sloping (depending on if she wins or loses) on the right.

b)

Gambler fallacy occurs when you believe that an event is less likely or more likely given a previous even but in actual they are independent event.

Here Randy's fourth child likelihood will be same for daughter or son irrespective of before event(3 son).

Law of larger number will applied on large set of events.

Answer : No, because Randy’s succumbing to the gambler’s fallacy.

Please revert back in case of any doubt.