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Q.

Suppose P is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and P has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval ?

A 8/(2e3)
B 9/(2e3)
C 17/(2e3)
D 26/(2e3)

Answer & Explanation

Answer: Option [C]

p is the number of cars per minute passing through a certain road junction.

The random variable P follows Poisson distribution with mean 3.

So, Prob(P = r)=gate-2013-question-3 - GkSeries

We have to determine probability of observing fewer than 3 cars.

So, r=0,1,2

Prob(P=0) + Prob(P=1) + Prob(P=2)

gate-2013-question-3-2 - GkSeries + gate-2013-question-3-3 - GkSeries + gate-2013-question-3-4 - GkSeries

=1/e3[1+3+9/2]

=17/2e3

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