DP Mathematics HL Questionbank
Cumulative distribution functions for both discrete and continuous distributions.
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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...
- 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 \(0 \leqslant t \leqslant 2\).
- 12M.3sp.hl.TZ0.4d: (i) Find the cumulative distribution function for X . (ii) Hence, or otherwise, find the...
- SPNone.2.hl.TZ0.3a: Complete the grouped frequency table for these data.
- SPNone.2.hl.TZ0.3b: Estimate the mean and standard deviation of the heights of these 80 boys.
- SPNone.2.hl.TZ0.3c: Explain briefly whether or not the normal distribution provides a suitable model for this...
- 13M.3sp.hl.TZ0.4a: (i) Determine an expression for \(F(x)\), valid for \(1 \leqslant x \leqslant 2\), where F...
- 11N.3sp.hl.TZ0.3d: Find the median of X in terms of \(\lambda \).
- 11N.3sp.hl.TZ0.3b: Find the cumulative distribution function, \(F(x)\), of X.
- 11N.3sp.hl.TZ0.3c: Find the probability that the lifetime of a particular battery is more than twice the mean.
- 11N.3sp.hl.TZ0.3e: Find the probability that the lifetime of a particular battery lies between the median and the mean.
- 11M.2.hl.TZ1.1a: Estimate the (i) median weight of the apples; (ii) 30th percentile of the weight of the...
- 11M.2.hl.TZ1.1b: Estimate the number of apples which weigh more than 110 grams.
- 15N.3sp.hl.TZ0.4a: Find \(F(u)\), the cumulative distribution function of \(U\), for...
- 15N.3sp.hl.TZ0.4b: Hence, or otherwise, find the value of \(P(U > 20)\).
- 14N.3sp.hl.TZ0.1c: Find the interquartile range for \(X\).
- 14N.3sp.hl.TZ0.1b: Find the cumulative distribution function for \(X\).
