Arjun Suresh (talk | contribs) |
Arjun Suresh (talk | contribs) |
||
| (10 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
| − | Suppose <math>p</math> is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and <math>p</math> has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval? | + | Suppose <math>p</math> is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and <math>p</math> 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) $8/(2e^{3})$ | (A) $8/(2e^{3})$ | ||
| Line 9: | Line 9: | ||
(D) $26/(2e^{3})$ | (D) $26/(2e^{3})$ | ||
| − | === | + | ==={{Template:Author|Arjun Suresh|{{arjunweb}} }}=== |
Poisson Probability Density Function (with mean $\lambda$) = $\lambda^{k} / (e^{\lambda}k!)$, | 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) | + | We have to sum the probability density function for $k = 0,1$ and $2$ and $\lambda$ = 3 (thus finding the cumulative mass function) |
| − | =$(1/e^3) + (3/e^3) + (9/ | + | =$(1/e^3) + (3/e^3) + (9/2e^3)$ |
=$17/(2e^{3})$ | =$17/(2e^{3})$ | ||
| − | + | {{Template:FBD}} | |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
[[Category: GATE2013]] | [[Category: GATE2013]] | ||
| − | [[Category: | + | [[Category: Probability questions from GATE]] |
Suppose <math>p</math> is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and <math>p</math> 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) $26/(2e^{3})$
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)
=$(1/e^3) + (3/e^3) + (9/2e^3)$
=$17/(2e^{3})$
Suppose <math>p</math> is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and <math>p</math> 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) $26/(2e^{3})$
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)
=$(1/e^3) + (3/e^3) + (9/e^3)$
=$17/(2e^{3})$
GATECSE