The probability that the price of Stock XYZ goes up after a day of trading is 0.
ID: 3201896 • Letter: T
Question
The probability that the price of Stock XYZ goes up after a day of trading is 0.3. hi 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. Does X 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 has 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
2)
(a)
(i) Here random experiment price of stock XYZ is Bernoulli trial i.e. price of stock XYZ will goes up or will non -increasing.
(ii)The Bernoulli trial is performed repeatedly a fixed number of times say 'n'.
(iii) All the trials are indedendent.
(iv) The probability of success (here success is price go up )in any trial is p=0.3 & is constant in each trial .
Since all condtions for Binomial experiment are satisfied, random variable X which represents number of days the stock will go up out of n=10 days folllows Binomial distribution with parameters n=10 & p=0.3
i.e. X ~ B(n=10,p=0.3).
P.M.F. of X is ,
P(X=x)=nCx px (1-p)n-x =10Cx 0.3x 0.710-x ; x=0,1,.......,n=10
(b) Expected number of days the stock will go up is given by ,
E(X) =np=10*0.3 =3
(c) The probability that the stock price goes up exactly 3 times in those 10 days is given by ,
P(X=3)= 10C3 0.33 0.710-3
=10C3 0.33 0.77
={10!/[3!*(10-3)!]}*0.027*0.0823543
={10*9*8*7!/[3!*7!]}*0.002223566
=120*0.002223566
=0.2668279
Thus, probability that the stock price goes up exactly 3 times in those 10 days is 0.2668279 .
(d) The probability that the stock price goes up atmost 2 of the 10 days is given by ,
P( X <=2) =P(X=0)+P(X=1)+P(X=2)
=10C0 0.30 0.710 +10C1 0.31 0.79 +10C2 0.32 0.78
={10!/[0!*(10-0)!]}*0.710 +{10!/[1!*(10-1)!]}*0.31 0.79+{10!/[2!*(10-2)!]}*0.32 0.78
={10!/[1*10!]}*0.710 +{10*9!/[1*9!]}*0.31 0.79+{10*9*8!/[2*1*8!]}*0.32 0.78
=0.710 +10*0.31 *0.79 +45*0.32 *0.78
=0.02824752+ 0.1210608+ 0.2334744
= 0.3827828
Thus , probability that the stock price goes up atmost 2 of the 10 days is 0.3827828.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.