The probability that the prier of Stock XYZ goes up after a day of trading is 0.

Question

The probability that the prier of Stock XYZ goes up after a day of trading is 0.3. In all other days, the price of Stock XYZ will either improve with stated probability or will go down or stay the same with a certain probability. We know that the direction of price movement in one day is not related to the direction of price movements in previous days (i.e. they are independent). Consider 10 consecutive days and let X count the number of days the stock will go up in those 10. Do times have a known distribution? If yes state, the distribution and give its parameters. What is the expected number of days in which the stock s price go up? (E[X]) What is the probability that the stock price goes up exactly 3 times in those 10 days? (P(X = 3)} What is the probability that the stock price goes up at most 2 of the 10 days? (P(X lessthanorequalto 2)} Given the same stock from problem 2, define now Y as the number of days until we see a stock increase (we count the day of the increase in Y): If Y lies a known type distribution state its name and give its parameters. What is the probability that the stock price goes up for the first time after 3 days? Give the expected number of days until stock goes up.

Explanation / Answer

Answer to question# 3)

Part a)

When the variable Y defines the number of days until the stock price rises, it is called geometric distribution. The only parameter of geometric distribution is Probability of success P

.

Part b)

Given p = 0.3

P(X=3) = (1-0.3)^3*0.3 = 0.1029

Thus the probability that the stock rises on the fourth day or as it is mentioned "after 3 days" is 0.1029

.

Answer to part c)

Expected number of days = 1 / p

Where p = probability of success

For this question p = 0.3 .........[Given]

Thus expected number of days = 1 / 0.3 = 3.33

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