9709 P53 - Nov 2023 - Q1
2887
Becky sometimes works in an office and sometimes works at home. The random variable \(X\) denotes the number of days that she works at home in any given week. It is given that
\(P(X = x) = kx(x+1)\),
where \(k\) is a constant and \(x = 1, 2, 3\) or \(4\) only.
(a) Draw up the probability distribution table for \(X\), giving the probabilities as numerical fractions.
(b) Find \(E(X)\) and \(\text{Var}(X)\).
