GATE CSE
First time here? Checkout the FAQ!
x
+2 votes
491 views
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) $8/(2e^{3})$

(B) $9/(2e^{3})$

(C) $17/(2e^{3})$

(D) $26/(2e^{3})$
asked in Probability by Veteran (12.6k points)  
retagged by | 491 views

1 Answer

+11 votes
Best answer
Poisson Probability Density Function (with mean $\lambda$) = $\lambda^{k} / (e^{\lambda}k!)$,

We have to sum the probability density function for $k = 0,1$ and $2$ and $\lambda$ = 3 (thus finding the cumulative mass function)

=$(1/e^3) + (3/e^3) + (9/2e^3)$

=$17/(2e^{3})$
answered by Veteran (273k points)  
selected by
Top Users Jan 2017
  1. Debashish Deka

    8608 Points

  2. sudsho

    5398 Points

  3. Habibkhan

    4718 Points

  4. Bikram

    4522 Points

  5. Vijay Thakur

    4468 Points

  6. saurabh rai

    4222 Points

  7. Arjun

    4122 Points

  8. santhoshdevulapally

    3742 Points

  9. Sushant Gokhale

    3576 Points

  10. GateSet

    3394 Points

Monthly Topper: Rs. 500 gift card

19,177 questions
24,073 answers
52,975 comments
20,310 users