(a) Show that for a Poisson distribution the mean is equal to the variance. (b) In a bakery 3600 sultanas are added to a mixture which is subsequently divided up to make 1200 fruit scones. Assuming that the number of sultanas in each scone follows a Poisson distribution, estimate (i) the number of scones which will be without a sultana; (ii) the number with 5 or more sultanas.
(a) Show that for a Poisson distribution the mean is equal to the variance. (b) In a bakery 3600 sultanas are added to a mixture which is subsequently divided up to make 1200 fruit scones. Assuming that the number of sultanas in each scone follows a Poisson distribution, estimate (i) the number of scones which will be without a sultana; (ii) the number with 5 or more sultanas.
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Statistics and Probability
Transcribed Image Text:(a) Show that for a Poisson distribution the mean is equal to the variance.
(b) In a bakery 3600 sultanas are added to a mixture which is subsequently divided up to make
1200 fruit scones. Assuming that the number of sultanas in each scone follows a Poisson
distribution, estimate
(i) the number of scones which will be without a sultana;
(ii) the number with 5 or more sultanas.
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