Anna is planning to invest 1000 euros for two years. She will choose between two savings accounts offered by the Nordea Bank of Finland:
- A standard fixed-term account which has a guaranteed interest rate of 5.5% after the two years
- A 'DepositPlus' account, for which the interest rate depends on the stock prices of three companies (Apple, Heineken and Wal-Mart) as follows:
- If the stock prices of all three companies are higher on 16 September 2013 than they were on 5 October 2011, the two-year interest rate is 8.1%.
- If not, the two-year interest rate is 1.1%.
Denote by X the two-year interest rate of the DepositPlus account, and by Y the two-year interest-rate of the standard account. Let pi denote the probability that the condition for the higher interst rate of the DepositPlus account is satisfied at the end of the period.
Calculate the expected value and standard deviation of X and the expected value and standard deviation of Y.
What I needed help with in this question was how to find the probability functions of X and Y, so any help would be greatly appreciated