Question: (a) If a variable has a Poisson distribution, determine its Mean, Variance. [3 Marks] (b) Highlight three differences between permutations and combinations. [3 Marks] (c)

(a) If a variable has a Poisson distribution, determine its Mean, Variance. [3 Marks] (b) Highlight three differences between permutations and combinations. [3 Marks] (c) The number of machine breakdowns in a large manufacturing firm during one week has the following summarised probability distribution: X 10 15 20 25 P(X=x) 0.25 0.30 0.25 0.15 0.05 Compute Var(3 - 5x) [10 Marks] (d) A certain machine manufactures motor vehicle parts. Given that the probability of the machine manufacturing a good part is 0.8, calculate the probability of finding 10 good parts in a sample of 12. [9 Marks]

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