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A factory produces two types of bulbs. Bulb 1 is produced with probability 0.6 and has...

A factory produces two types of bulbs. Bulb 1 is produced with probability 0.6 and has a lifetime which is geometrically distributed with parameter 0.2. Bulb 2 is produced with probability 0.4 and has a lifetime which is geometrically distributed with parameter 0.4. Let X be the lifetime of a device produced by the factory. What is the mean and variance of X ? Note: For a geometric distribution with parameter p, P(X = k) = (1 − p) k−1p, k ∈ {1, 2, 3, . . .}.

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The life of the bulb is given by the random variable

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