Stuck at an exponential distribution assignment
So I have a small question when it comes to probability and the Exponential Distribution.
The assignment states the following:
Clients arrive on a counter independently from one-another. The time between two arrivals has an exponential distribution with a parameter 1/6. Let X be the random variable that defines the time between two arrivals.
One client has just arrived on the counter. Find the probability that the next client will arrive for more than 15 minutes.
I think I know the answer but I'm not sure.
I think I'm suppose to solve P{X>15} but I'm not sure. Is this the right answer?
probability
asked 2 days ago
David MathersDavid Mathers
193
add a comment |
So I have a small question when it comes to probability and the Exponential Distribution.
The assignment states the following:
Clients arrive on a counter independently from one-another. The time between two arrivals has an exponential distribution with a parameter 1/6. Let X be the random variable that defines the time between two arrivals.
One client has just arrived on the counter. Find the probability that the next client will arrive for more than 15 minutes.
I think I know the answer but I'm not sure.
I think I'm suppose to solve P{X>15} but I'm not sure. Is this the right answer?
probability
asked 2 days ago
David MathersDavid Mathers
193
Do you mean, "will NOT arrive for more than 15 minutes"? If so, the answer is $e^{-15/6}$, which follows directly from the exponential distribution.
– Math1000
2 days ago
Yes that was what I meant. Is my answer correct?
– David Mathers
2 days ago
add a comment |
So I have a small question when it comes to probability and the Exponential Distribution.
The assignment states the following:
Clients arrive on a counter independently from one-another. The time between two arrivals has an exponential distribution with a parameter 1/6. Let X be the random variable that defines the time between two arrivals.
One client has just arrived on the counter. Find the probability that the next client will arrive for more than 15 minutes.
I think I know the answer but I'm not sure.
I think I'm suppose to solve P{X>15} but I'm not sure. Is this the right answer?
probability
asked 2 days ago
David MathersDavid Mathers
193
So I have a small question when it comes to probability and the Exponential Distribution.
The assignment states the following:
Clients arrive on a counter independently from one-another. The time between two arrivals has an exponential distribution with a parameter 1/6. Let X be the random variable that defines the time between two arrivals.
One client has just arrived on the counter. Find the probability that the next client will arrive for more than 15 minutes.
I think I know the answer but I'm not sure.
I think I'm suppose to solve P{X>15} but I'm not sure. Is this the right answer?
probability
probability
asked 2 days ago
David MathersDavid Mathers
193
asked 2 days ago
David MathersDavid Mathers
193
asked 2 days ago
David MathersDavid Mathers
193
asked 2 days ago
David MathersDavid Mathers
193
asked 2 days ago
David MathersDavid Mathers
193
193
Do you mean, "will NOT arrive for more than 15 minutes"? If so, the answer is $e^{-15/6}$, which follows directly from the exponential distribution.
– Math1000
2 days ago
Yes that was what I meant. Is my answer correct?
– David Mathers
2 days ago
add a comment |
Do you mean, "will NOT arrive for more than 15 minutes"? If so, the answer is $e^{-15/6}$, which follows directly from the exponential distribution.
– Math1000
2 days ago
Yes that was what I meant. Is my answer correct?
– David Mathers
2 days ago
Do you mean, "will NOT arrive for more than 15 minutes"? If so, the answer is $e^{-15/6}$, which follows directly from the exponential distribution.
– Math1000
2 days ago
Do you mean, "will NOT arrive for more than 15 minutes"? If so, the answer is $e^{-15/6}$, which follows directly from the exponential distribution.
– Math1000
2 days ago
Yes that was what I meant. Is my answer correct?
– David Mathers
2 days ago
Yes that was what I meant. Is my answer correct?
– David Mathers
2 days ago
add a comment |
1 Answer
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Assuming the events we are concerned about are modeled by means of a random variable X that follows an exponential distribution with rate $lambda=frac{1}{6}$ (which expresses the frequency of arrivals per minute), to find the probability that the time that elapses between the arrival of two clients is greater than 15 minutes, indeed, you need to find $P(X)>15$.
(Although you do not ask about the solution, recall that the cumulative distribution function $F(x)$ of $X$ is given by $1-e^{-lambda,x}$. With that in mind finding the solution is straightforward).
answered 2 days ago
DavidPMDavidPM
28118
add a comment |
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1 Answer
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1 Answer
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active
oldest
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oldest
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Assuming the events we are concerned about are modeled by means of a random variable X that follows an exponential distribution with rate $lambda=frac{1}{6}$ (which expresses the frequency of arrivals per minute), to find the probability that the time that elapses between the arrival of two clients is greater than 15 minutes, indeed, you need to find $P(X)>15$.
(Although you do not ask about the solution, recall that the cumulative distribution function $F(x)$ of $X$ is given by $1-e^{-lambda,x}$. With that in mind finding the solution is straightforward).
answered 2 days ago
DavidPMDavidPM
28118
add a comment |
Assuming the events we are concerned about are modeled by means of a random variable X that follows an exponential distribution with rate $lambda=frac{1}{6}$ (which expresses the frequency of arrivals per minute), to find the probability that the time that elapses between the arrival of two clients is greater than 15 minutes, indeed, you need to find $P(X)>15$.
(Although you do not ask about the solution, recall that the cumulative distribution function $F(x)$ of $X$ is given by $1-e^{-lambda,x}$. With that in mind finding the solution is straightforward).
answered 2 days ago
DavidPMDavidPM
28118
add a comment |
Assuming the events we are concerned about are modeled by means of a random variable X that follows an exponential distribution with rate $lambda=frac{1}{6}$ (which expresses the frequency of arrivals per minute), to find the probability that the time that elapses between the arrival of two clients is greater than 15 minutes, indeed, you need to find $P(X)>15$.
(Although you do not ask about the solution, recall that the cumulative distribution function $F(x)$ of $X$ is given by $1-e^{-lambda,x}$. With that in mind finding the solution is straightforward).
answered 2 days ago
DavidPMDavidPM
28118
Assuming the events we are concerned about are modeled by means of a random variable X that follows an exponential distribution with rate $lambda=frac{1}{6}$ (which expresses the frequency of arrivals per minute), to find the probability that the time that elapses between the arrival of two clients is greater than 15 minutes, indeed, you need to find $P(X)>15$.
(Although you do not ask about the solution, recall that the cumulative distribution function $F(x)$ of $X$ is given by $1-e^{-lambda,x}$. With that in mind finding the solution is straightforward).
answered 2 days ago
DavidPMDavidPM
28118
answered 2 days ago
DavidPMDavidPM
28118
answered 2 days ago
DavidPMDavidPM
28118
answered 2 days ago
DavidPMDavidPM
28118
28118
add a comment |
add a comment |
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Do you mean, "will NOT arrive for more than 15 minutes"? If so, the answer is $e^{-15/6}$, which follows directly from the exponential distribution.
– Math1000
2 days ago
Yes that was what I meant. Is my answer correct?
– David Mathers
2 days ago