(DISCRETE RANDOM VARIABLE)
An option to buy a stock is priced at $200. If the stock closes above 30, the option will be worth $1000. If it closes below 20, the option will be worth nothing. If it closes between 20 and 30 (inclusive), then the option will be worth $200. A trader thinks there is 50% chance that the stock will close in the 20 - 30 range and a 30% chance that it will close below 20.
1. How much does the trader expect to gain?
2. What is the standard deviation of her gain?
3. Do you think the trader should buy the stock option? Explain your choice in two sentences.