DP Mathematics HL Questionbank

Probability generating functions for discrete 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′(t).
- 18M.3sp.hl.TZ0.2b: Show that the probability generating function, G(t), 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, GX+Y(t), of X+Y, show that...
- 17N.3sp.hl.TZ0.5a.ii: Hence show that Var(X)=λ.
- 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⩽t⩽2, clearly indicating the...
- 17N.3sp.hl.TZ0.1a: Find the cumulative distribution function F(t), for 0⩽t⩽2.
- SPNone.3sp.hl.TZ0.2b: Show that the probability generating function for X is given...
- SPNone.3sp.hl.TZ0.2c: Hence determine 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 X1 and X2 are such that...
- 15M.3sp.hl.TZ0.5a: Determine the probability generating function for X∼B(1, p).
- 15M.3sp.hl.TZ0.5b: Explain why the probability generating function for B(n, p) is a polynomial...
- 14N.3sp.hl.TZ0.4a: (i) Prove that E(X)=λ. (ii) Prove that...
- 14N.3sp.hl.TZ0.4e: By consideration of the probability generating function, GX+Y(t), of X+Y, prove...
- 14N.3sp.hl.TZ0.4g: Hence find the probability that X+Y is an even number.