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An investor buys the stock of ten companies, investing $10 in each. The stock of each company either goes up by 80% after a month (rising to $18) with probability 1/3 or drops by 60% (falling to $4) with probability 2/3. Assume that the changes in each are independent. Let the random variable X denote the value of the amount invested after one month.
1. P(X = 40) = ?
(a) (1/3)^10 (b) ( 1⁄2)^6 (c) (2/3)10 (d) (1/3)^5 * (2/3)^5
2. The mean of X is
(a) 11 (b) 8/3 (c) 26/3 (d) 260/3
3. Find the standard deviation of X ?
(a) 65.99 (b) 43.56 (c) 32 (d) none of the above
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