10. A traffic control engineer reports that 75% of the vehicles passing through

Question

10. A traffic control engineer reports that 75% of the vehicles passing through a checkpoint are from within the state. What is the probability that fewer than 4 of the next 9 vehicles are from out of state? 11. A certain area of eastern United States is, on average, hit by 6 hurricanes a year. Find the probability that in a given year that area will be hit by few than 4 hurricanes. 12. Suppose X and Y are independent Poisson random variables with param- eters 1 and 2 respectively. Find the distributions of X +Y and X +2Y. 13. Suppose X and Y are independent uniform random variables on the same interval [0, 1]. What is the probability that X- Yl2 1/2?

Explanation / Answer

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Q10)

We model using the binomial pdf function. All calculations are below:

p( pass)= .75

n = 9

P(X<4)

= P(X=0,1,2,3)

= 9C0(.75^0)*(.25^9) + 9C1(.75^1)*(.25^8) +9C2(.75^2)*(.25^7) +9C3(.75^3)*(.25^6)

= 0.0099

So, probability that fewer than 4 out of next 9 vehicles are out of state is .0099 or .99%

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