Please I need all the details. 11. (4+4 pts) Suppose you have two stocks. Every
ID: 3320460 • Letter: P
Question
Please I need all the details.
11. (4+4 pts) Suppose you have two stocks. Every day, stock #1, a utility, will have a change in value that can be approximated by a normal distribution with mean +$5 and standard deviation 3. Every day, stock #2, a small software firm, will have a change in value that can approximated by a normal distribution with mean +$10 and standard deviation 4. (Note that the change in value of either stock can be negative.) a) (4 pts) What is the probability that we will make money tomorrow? That is, what is the probability that the sum of the changes in value is greater than or equal to zero? Answer: b) (4 pts) Let X be the number of days in the following week on which you make money. Find P(X 23), E[X], and Var(X) Answer:Explanation / Answer
a.
as it is given that Stock 1 has mean = 5$ and sd=3
while Stock 2 has mean = 10$ and sd=4
We need to find the prob of making money and so here the mean of both combined is = 5+10= 15$ above which we will make money
Now sd of the combined shares 1 & 2 is nothing but = sqrt(variance of share 1 + variance of share 2)
= sqrt(3^2 + 4^2)= sqrt(25) = 5
so now we have sd = 5 and mean = 15 for the combined distribution
Now you are bound to gain if mean > 15 and so if we plot the same on the normal cureve with N(15,5) we will get mean>15 with probability of 0.5 as we know that the distribution is symmetric across its mean and so we fimly stat that 50% is the probability of sum of changes > 0
b) now in a week we have 7 days but the stock market works on 5 days only and 2 days it remains closed and so the P(X>=3) = P(X=3)+P(X=4)+P(X=5)
and we have n=5 days of a week with p =0.5 i.e. prob of success and q=1-0.5 =0.5
So applying the binomial theorm we get
P(X=3) = 5C3 * 0.5^3 * 0.5^2 now for
P(X=4) = 5C4 * 0.5^4 * 0.5^1 now for
P(X=5) = 5C5 * 0.5^5 * 0.5^0 and summing up all we get
P(X>=3) = P(X=3)+P(X=4)+P(X=5) = 0.5
and so we say that prob is 0.5 and E(X) is the mean i.e. 15 and we know sd(x) = 5 and so var(x) = sd(x)^2 = 5^2 =25
Hope the above explaination has helped you in understanding the problem Pls upvote the ans if it has really helped you. Good Luck!!