DP Mathematics HL Questionbank

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Directly related questions

• 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...
• 16N.3sp.hl.TZ0.4b: By differentiating \(J(t)\), prove that (i)    ...
• 16N.3sp.hl.TZ0.4a: Write down an expression for \(J(t)\) in terms of \(G(t)\) and \(H(t)\).
• 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 \(0 \leqslant t \leqslant 2\).
• SPNone.3sp.hl.TZ0.2b: Show that the probability generating function for X is given...
• SPNone.3sp.hl.TZ0.2c: Hence determine \({\text{E}}(X)\).
• 15N.3sp.hl.TZ0.4c: Prove that the probability generating function of \(U\) is given by...
• 15M.3sp.hl.TZ0.5c: Two independent random variables \({X_1}\) and \({X_2}\) are such that...
• 15M.3sp.hl.TZ0.5a: Determine the probability generating function for \(X \sim {\text{B}}(1,{\text{ }}p)\).
• 15M.3sp.hl.TZ0.5b: Explain why the probability generating function for \({\text{B}}(n,{\text{ }}p)\) is a polynomial...
• 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.TZ0.4g: Hence find the probability that \(X + Y\) is an even number.