May/June 2026 Paper 61

2026 · 6 questions · 17 parts · 50 marks

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Context for 5(a)

X

and

Y

are independent random variables such that

X \sim Po (2.5)

and

Y \sim Po (λ)

5(a)(i)Poisson DistributionMedium2 marks

Find

P (1 \leq X \leq 3)

Probability

5(a)(ii)Poisson DistributionHard4 marks

Given that

P (X = 5) = P (X + Y = 0)

, find

P (X + Y = 1)

Show your working

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Probability

5(b)Poisson DistributionHard4 marks

The random variable

W

has the distribution

B (200, 0.02)

. It is given that, using the binomial distribution,

P (W = 2) = 0.146

, correct to 3 decimal places.

Show that a suitable approximating distribution gives the same value of

P (W = 2)

correct to 2 decimal places, but not correct to 3 decimal places.

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