Question

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) distribution
• the number of Japanese-made cars J has the Poisson (5) distribution
• the number of all other cars X has the Poisson (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) 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 ?(?=?). It is all right to have infinite sums in this one.

c) Write a math expression for ?(?=20)

Answer 1