Question

Probability! My prof said it is related to variance but have no idea..

You plan to invest $200,000 in stocks on the Toronto Stock Exchange. If you invest
$2000 in any particular stock, your profit will be $400, $200, $0 or -$200 (a loss)
with probability 0.25 each. There are 100 different stocks you can choose from, and
they all behave independently of each other.

(a)
If you invest $200,000 in one stock, what is the probability that your profit will
be $15,000 or more.

(b)
If you invest $2000 in each of the 100 stocks, what is the probability that your
profit will be $15,000 or more.

Answer 1

Oh not sure about b) but I think a) is correct, since it makes sense to me!
Thank you!!

Answer 2

I am taking statistic class too, but why could I not answer? haha
Anyway, thanks! If u can do part b) please reply me too!

Answer 3

yeah that s fine. Thanks!

Answer 4

For part A, first find the expected return... which represents the mean
then find the standard deviation

Answer 5

For part B, find the mean and variance for 1
$2000 purchase

all 100 purchases have independent statistics. Find the mean
then find the variance of the mean
https://en.wikipedia.org/wiki/Variance#Sum_of_uncorrelated_variables_.28Bienaym.C3.A9_formula.29

Answer 6

For example, in part A, you have 4 equally likely (at 0.25 chance) outcomes
10,000, 5,000 , 0, -5,000

Can you find the expected value ?

the variance will be E(x^2) - ( E(x) )^2

the std dev = sqr(variance)

finally see how far 15,000 is above the mean (i.e. the expected value) in terms of the std
use a table to find the probability.