DP Mathematics HL Questionbank
Using probability generating functions to find mean, variance and the distribution of the sum of \(n\) independent random variables.
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- 18M.3sp.hl.TZ0.2d: Determine the mean number of throws required to obtain a 1.
- 18M.3sp.hl.TZ0.2c: Find \(G'\left( t \right)\).
- 18M.3sp.hl.TZ0.2b: Show that the probability generating function, \(G\left( t \right)\), for X is given by...
- 18M.3sp.hl.TZ0.2a: State the distribution of X.
- 16M.3sp.hl.TZ0.5b: (i) Show that \(G(t)\), the probability generating function of \(Y\), is given by...
- 16M.3sp.hl.TZ0.5a: Show that the probability distribution of \(Y\) is given by...
- 17N.3sp.hl.TZ0.5c.ii: Identify the probability distribution given in part (c)(i) and state its parameters.
- 17N.3sp.hl.TZ0.5c.i: Show...
- 17N.3sp.hl.TZ0.5b: By considering the probability generating function, \({G_{X + Y}}(t)\), of \(X + Y\), show that...
- 17N.3sp.hl.TZ0.5a.ii: Hence show that \({\text{Var}}(X) = \lambda \).
- 17N.3sp.hl.TZ0.5a.i: Find expressions for \({G’_X}(t)\) and \({G’’_X}(t)\).
- 17N.3sp.hl.TZ0.1b.ii: Given that \(P(T < a) = 0.75\), find the value of \(a\).
- 17N.3sp.hl.TZ0.1b.i: Sketch the graph of \(F(t)\) for \(0 \leqslant t \leqslant 2\), clearly indicating the...
- 17N.3sp.hl.TZ0.1a: Find the cumulative distribution function \(F(t)\), for \(0 \leqslant t \leqslant 2\).
- 15N.3sp.hl.TZ0.4e: A third random variable \(W\), has probability generating function...
- 15N.3sp.hl.TZ0.4f: A third random variable \(W\), has probability generating function...
- 14N.3sp.hl.TZ0.4a: (i) Prove that \({\text{E}}(X) = \lambda \). (ii) Prove that...
- 14N.3sp.hl.TZ0.4e: By consideration of the probability generating function, \({G_{X + Y}}(t)\), of \(X + Y\), prove...
- 14N.3sp.hl.TZ0.4f: Find (i) \({G_{X + Y}}(1)\); (ii) \({G_{X + Y}}( - 1)\).
