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 $0 \leqslant t \leqslant 2$.
• 12M.3sp.hl.TZ0.2c: Given that p = 0.2, find the least value of n for which...
• 12M.3sp.hl.TZ0.2a: Show that ${\text{P}}(X \leqslant n) = 1 - {(1 - p)^n},{\text{ }}n \in {\mathbb{Z}^ + }$ .
• 12M.3sp.hl.TZ0.2b: Deduce an expression for...
• 12N.3sp.hl.TZ0.4a: If the dice is fair, write down the distribution of X , including the value of any parameter(s).
• 12N.3sp.hl.TZ0.4b: Write down E(X ) for the distribution in part (a).
• 08M.3sp.hl.TZ1.5: (a)     Having thrown the die once, she lets ${X_2}$ denote the number of additional throws...
• 09M.3sp.hl.TZ0.4: In a game there are n players, where $n > 2$ . Each player has a disc, one side of which is...
• 14M.3sp.hl.TZ0.4: Consider the random variable $X \sim {\text{Geo}}(p)$. (a)     State \({\text{P}}(X <...
• 15N.3sp.hl.TZ0.4a: Find $F(u)$, the cumulative distribution function of $U$, for...