Consider a random variable X with probability density function (PDF) given by if x ≥2 otherwise fx(x)= 0 where c> 0 is an as-of-yet undetermined constant. (a) Find the value of c that ensures the function fx(x) is a valid PDF. (b) Compute P(1 ≤X ≤ 4). (c) Compute P(X≥ 5 | X≥ 3). (d) Compute E[X]. (e) Compute Var (X). (f) Find Fx (x), the cumulative distribution function (CDF) of X.

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