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Assume the number of episodes per year of a disease follow Poisson distribution with parameter $u=1.6$ per year.

1) What is the probability that two siblings will both have three or more episodes of disease in the first two years of life?

ans: $u=1.6^2\text{ (times 2 because 2 year)}=3.2$, so $P(X\ge3) \cdot P(X\ge3) = [1-P(X=0)-P(X=1)-P(X=2)]^2$ by applying $u=3.2$

2) what is the probability that exactly one siblings will have three or more episodes of disease in the first two years of life?

ans: $u=1.6^2\text{ (times 2 because 2 year)}=3.2$, so $P(X\ge3)= 1-P(X=0)-P(X=1)-P(X=2)$ by applying $u=3.2$

3) what is the expected number of siblings, in a 2-sibling family, who will have three or more episodes in the first two years of life?

May anyone help me solve the question 3? help me check whether question 1 and 2 are correct?

Thanks.

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    noob: Changed $P$ to $X$ thrice in your post. Tell me if this is OK.2011-09-27

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