CAIE S2 2014 June — Question 8

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2014
SessionJune
TopicPoisson Distribution
TypeFrequency distribution and Poisson fit
8
  1. The following tables show the probability distributions for the random variables \(V\) and \(W\).
    \(v\)- 101\(> 1\)
    \(\mathrm { P } ( V = v )\)0.3680.3680.1840.080
    \(w\)00.51\(> 1\)
    \(\mathrm { P } ( W = w )\)0.3680.3680.1840.080
    For each of the variables \(V\) and \(W\) state how you can tell from its probability distribution that it does NOT have a Poisson distribution.
  2. The random variable \(X\) has the distribution \(\operatorname { Po } ( \lambda )\). It is given that $$\mathrm { P } ( X = 0 ) = p \quad \text { and } \quad \mathrm { P } ( X = 1 ) = 2.5 p$$ where \(p\) is a constant.
    (a) Show that \(\lambda = 2.5\).
    (b) Find \(\mathrm { P } ( X \geqslant 3 )\).
  3. The random variable \(Y\) has the distribution \(\operatorname { Po } ( \mu )\), where \(\mu > 30\). Using a suitable approximating distribution, it is found that \(\mathrm { P } ( Y > 40 ) = 0.5793\) correct to 4 decimal places. Find \(\mu\).
This paper (8 questions)
View full paper
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8