Question: 1. A random variable X has a continuous distribution with the following probability density function: kx(3-x) for 0x3 f(x) = o otherwise. (a) Find

1. A random variable X has a continuous distribution with the following probability density function: kx(3-x) for 0x3 f(x) = o otherwise. (a) Find the value of the constant k. (b) Determine the expected value of X, i.e. E(X). (c) Determine the variance of X, i.e. Var(X). (d) Determine the cumulative distribution function (cdf), F(x).

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