Question

Describe a general sample space for the following situations:

a) Stock of company A is currently selling for $100 a share. The time until the stock reaches $300.

b) Price of stock of companies A and B.

Answer 1

A sample space is the range of values of a random variable.

a) Stock of company A is currently selling for $100 a share. The time until the stock reaches $300.Where we are looking for the value of time which could be any positive integer.

So the time until the stock reaches 300$ can have values from 0 to inf which serves as a sample space

If there is a function given for time like., S=So * e^-rt where S=300 , So=100 and r is the risk rate then you can calculate all the possible values of t which becomes your sample space. Since no such function is provided here the sample space is [0,inf)

b) Price of stock of companies A and B and also take values from 0 to inf [0,inf)

and hence the sample space for the same is also [0,inf)

Here as well there is no function is provided for stock price and hence the sample space is [0,inf)

Hope the above answer has helped you in understanding the problem. Please upvote the ans if it has really helped you. Good Luck!!