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 \(0 \leqslant t \leqslant 2\).
• 12N.3sp.hl.TZ0.4d: Before Jenny’s Dad can start, he has to throw two “sixes” using a fair, ordinary six-sided dice....
• 12N.3sp.hl.TZ0.4e: Before Jenny’s Dad can start, he has to throw two “sixes” using a fair, ordinary six-sided dice....
• 12N.3sp.hl.TZ0.4f: Before Jenny’s Dad can start, he has to throw two “sixes” using a fair, ordinary six-sided dice....
• 08N.3sp.hl.TZ0.3: (a)     The heating in a residential school is to be increased on the third frosty day during the...
• 11M.3sp.hl.TZ0.5b: Jo has a biased coin which has a probability of 0.35 of showing heads when tossed. She tosses...
• 11M.3sp.hl.TZ0.5a: The random variable X has the negative binomial distribution NB(3, p) . Let \(f(x)\) denote the...
• 10M.3sp.hl.TZ0.5b: The random variable X has the negative binomial distribution NB(5, p), where p < 0.5, and...
• 10N.3sp.hl.TZ0.3: As soon as Sarah misses a total of 4 lessons at her school an email is sent to her parents. The...
• 13M.3sp.hl.TZ0.5a: Find the probability that (i)     he hits the target exactly 4 times in his first 8 shots; (ii)...
• 13M.3sp.hl.TZ0.5b: Ben hits the target for the \({10^{{\text{th}}}}\) time with his \({X^{{\text{th}}}}\) shot. (i)...
• 14N.3sp.hl.TZ0.2b: (i)     Find the expected number of throws required for Eric to hit the target three times. (ii)...
• 14N.3sp.hl.TZ0.2c: If he has just \($8\), find the probability he will lose all his money before he hits the target...