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The probability density function of the random variable X is given by fX(x) = ax +...

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Basic Math

The probability density function of the random variable X isgiven by fX(x) = ax + 2/9 if 1/2 ? x ? 3, and 0 otherwise.

(a) Compute the value of a.

(b) Let the random variable Y be defined as Y = [X], where [·]is the “round down” operator (that is, for example, [2.5] = 2,[?2.5] = ?3, [?3] = ?3). Find the probability mass function of Y .(Hint: For Y to take value k, what values should X take?)

(c) Compute Var(Y )

I am confused with part B.

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