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3. A small manufacturing firm sells 1 machine per month with probability 0.3; it sells 2 machines per month with probability 0.1; it never

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3. A small manufacturing firm sells 1 machine per month with probability 0.3; it sells 2 machines per month with probability 0.1; it never sells more than 2 machines per month. If X represents the number of machines sold per month, (a) find the mean and variance of X. (b) If the monthly profit is 2x +3X+ 1 (in thousands of dollars), find the expected monthly profit.

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