Jim likes to day-trade on the Internet. On a good day, he averages a $1100 gain. On a bad day , he averages a $900 loss. Suppose that he has good days 25% of the time, bad days 35% of the time, the rest of the time he breaks even. a. What is the expected value of one day of Jim’s day-trading hobby ? b. If Jim day-trades every weekday for three weeks , how much money should he expect to win or lose?
We are given with:
On a good day, gain is $1100. The probability of being a good day is 25%.
On a bad day, loss is $900. The probability of being a bad day is 35%.
Rest of the days is break even. Break even is the point where no gain and no loss. The probability of break even is 100%-(25%+35%)=40%
So, we can make a table for the amount and it’s probability.
Amount(gain/loss) (x) $1100 -$900 0
Probability P(x) 25% 35% 40%
Expected value formula is E(x)=Xi *P(Xi)
So, we can answer the first part of the problem:
Expected value E(x) =$1100(25%) +(-$900)(35%) +0(40%)
Let’s change each percent to decimal by divide the percent by 100.
So, E(x) = $1100(0.25) +(-$900)(0.35)+0(0.40)
E(x) = -$40
So, Answer to part A is $40.
Jim is doing trade for 3 week in weekdays. There are 5 days in a week day. So, in 3 weeks there are 15 days.
So, multiply the 15 and expected value to get how much money he expected to win or loss.
-$40 x 15=-$600
It means that , Jim expected to loss $600.