Question

Data indicates that the number of traffic accidents on a rainy day is Poisson with mean 19, while on a dry day, it is Poisson with mean 13. Let X denote the number of traffic accidents tomorrow. Suppose that the chance it rains tomorrow is 0.6. Find(a)P(rain tomorrow|X= 15) using Bayes rule. (b)E(X).

Answer #1

**a)P(rain tomorrow|X= 15) using Bayes rule as consider
by:**

= P(X=15)

= P(X=15 and rainy day) + P(X=15 and dry day)

=
(e^-19*19^15/15! ) *0.6 + ( e^-13*13^15/15!)*0.4

= 0.0650*0.6 + 0.0885*0.4

= 0.07441673

P (rain tomorrow|X= 15) = 0.0650*0.6/0.07441673

**=
0.5244**

**Therefore,**

**P(x =15) = 0.5244**

**b) E(X) as
consider by:**

E(x) = 19*0.6+13*0.4

= 16.6

**Therefore,**

**E(x) =
16.6**

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