4. Cars at a Crossing Chendi sits at a cafe for 30 minutes sipping tea and...

4. Cars at a Crossing

Chendi sits at a cafe for 30 minutes sipping tea and watching cars go by. Assume:

the number of US-made cars ?U has the Poisson (7)(7) distribution
the number of Japanese-made cars ?J has the Poisson (5)(5) distribution
the number of all other cars ?X has the Poisson (4)(4) distribution

Assume also that ?U, ?J, and ?X are independent of each other, and let the total number of cars be ?=?+?+?T=U+J+X.

Some parts below ask for numerical values as well as math expressions. There is a code cell at the end of the exercise for numerical computations.

a) Write a math expression for ?(?≥9,?≥9)P(U≥9,J≥9) that does not include any infinite sums. Then use the code cell to find its numerical value, and provide the numerical value along with your expression.

b) Write a math expression for ?(?=?)P(J=X). It is all right to have infinite sums in this one.

c) Write a math expression for ?(?=20)P(T=20), and provide its numerical value by using the code cell below.

Expert Solution

orchestra answered 1 year ago

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