GATE CSE
First time here? Checkout the FAQ!
x
+2 votes
647 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 (12.9k points)  
retagged by | 647 views

1 Answer

+12 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 (280k points)  
selected by
Top Users Feb 2017
  1. Arjun

    5166 Points

  2. Bikram

    4204 Points

  3. Habibkhan

    3748 Points

  4. Aboveallplayer

    2986 Points

  5. sriv_shubham

    2298 Points

  6. Debashish Deka

    2234 Points

  7. Smriti012

    2142 Points

  8. Arnabi

    1998 Points

  9. mcjoshi

    1626 Points

  10. sh!va

    1552 Points

Monthly Topper: Rs. 500 gift card

20,815 questions
25,974 answers
59,606 comments
22,025 users