Solution Found!
Answer: A simplified model for the movement of the price
Chapter 3, Problem 58P(choose chapter or problem)
Problem 58P
A simplified model for the movement of the price of a stock supposes that on each day the stock’s price either moves up 1 unit with probability p or moves down 1 unit with probability 1 − p.The changes on different days are assumed to be independent.
(a) What is the probability that after 2 days the stock will be at its original price?
(b) What is the probability that after 3 days the stock’s price will have increased by 1 unit?
(c) Given that after 3 days the stock’s price has increased by 1 unit, what is the probability that it went up on the first day?
Questions & Answers
QUESTION:
Problem 58P
A simplified model for the movement of the price of a stock supposes that on each day the stock’s price either moves up 1 unit with probability p or moves down 1 unit with probability 1 − p.The changes on different days are assumed to be independent.
(a) What is the probability that after 2 days the stock will be at its original price?
(b) What is the probability that after 3 days the stock’s price will have increased by 1 unit?
(c) Given that after 3 days the stock’s price has increased by 1 unit, what is the probability that it went up on the first day?
ANSWER:
Step 1 of 4
Let p = each day the stock’s price either moves up 1 unit, and
1 - p = each day the stock’s price either moves down 1 unit.
The changes on different days are assumed to be independent.