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?

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:

Part:A

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)

=$275-$315+$0

E(x) = -$40

So, Answer to part A is $40.

Part B:

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.

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