Mixing
Stuck at an exponential distribution task
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So I'm given an assignment in probability that states the following:
A standard bus during one trip spends a quantity of fuel that has an Exponential distribution with an expected fuel used of 8 gallons.
Suppose during the day the bus makes 60 trips. Find the least fuel that needs to be supplied in a day so that that amount will sustain the bus with a probability of not lesser that 0.937.
Any ideas?
probability
asked Jan 9 at 1:17
David MathersDavid Mathers
163
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add a comment |
$begingroup$
So I'm given an assignment in probability that states the following:
A standard bus during one trip spends a quantity of fuel that has an Exponential distribution with an expected fuel used of 8 gallons.
Suppose during the day the bus makes 60 trips. Find the least fuel that needs to be supplied in a day so that that amount will sustain the bus with a probability of not lesser that 0.937.
Any ideas?
probability
asked Jan 9 at 1:17
David MathersDavid Mathers
163
$endgroup$
$begingroup$
If $X_i$ is the amount used on trip $i$ and if the trips are independent, then $X_1 + ldots + X_{60}$ has a gamma distribution with $alpha=60$ and rate $1/8$. The functionqgammain R can be used to complete the computation. See math.stackexchange.com/q/2383885 for clarification on the rate vs scale parametrization.
$endgroup$
– Just_to_Answer
Jan 9 at 4:18
add a comment |
$begingroup$
So I'm given an assignment in probability that states the following:
A standard bus during one trip spends a quantity of fuel that has an Exponential distribution with an expected fuel used of 8 gallons.
Suppose during the day the bus makes 60 trips. Find the least fuel that needs to be supplied in a day so that that amount will sustain the bus with a probability of not lesser that 0.937.
Any ideas?
probability
asked Jan 9 at 1:17
David MathersDavid Mathers
163
$endgroup$
So I'm given an assignment in probability that states the following:
A standard bus during one trip spends a quantity of fuel that has an Exponential distribution with an expected fuel used of 8 gallons.
Suppose during the day the bus makes 60 trips. Find the least fuel that needs to be supplied in a day so that that amount will sustain the bus with a probability of not lesser that 0.937.
Any ideas?
probability
probability
asked Jan 9 at 1:17
David MathersDavid Mathers
163
asked Jan 9 at 1:17
David MathersDavid Mathers
163
asked Jan 9 at 1:17
David MathersDavid Mathers
163
asked Jan 9 at 1:17
David MathersDavid Mathers
163
asked Jan 9 at 1:17
David MathersDavid Mathers
163
163
$begingroup$
If $X_i$ is the amount used on trip $i$ and if the trips are independent, then $X_1 + ldots + X_{60}$ has a gamma distribution with $alpha=60$ and rate $1/8$. The functionqgammain R can be used to complete the computation. See math.stackexchange.com/q/2383885 for clarification on the rate vs scale parametrization.
$endgroup$
– Just_to_Answer
Jan 9 at 4:18
add a comment |
$begingroup$
If $X_i$ is the amount used on trip $i$ and if the trips are independent, then $X_1 + ldots + X_{60}$ has a gamma distribution with $alpha=60$ and rate $1/8$. The functionqgammain R can be used to complete the computation. See math.stackexchange.com/q/2383885 for clarification on the rate vs scale parametrization.
$endgroup$
– Just_to_Answer
Jan 9 at 4:18
$begingroup$
If $X_i$ is the amount used on trip $i$ and if the trips are independent, then $X_1 + ldots + X_{60}$ has a gamma distribution with $alpha=60$ and rate $1/8$. The function
qgamma in R can be used to complete the computation. See math.stackexchange.com/q/2383885 for clarification on the rate vs scale parametrization.$endgroup$
– Just_to_Answer
Jan 9 at 4:18
$begingroup$
If $X_i$ is the amount used on trip $i$ and if the trips are independent, then $X_1 + ldots + X_{60}$ has a gamma distribution with $alpha=60$ and rate $1/8$. The function
qgamma in R can be used to complete the computation. See math.stackexchange.com/q/2383885 for clarification on the rate vs scale parametrization.$endgroup$
– Just_to_Answer
Jan 9 at 4:18
add a comment |
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$begingroup$
If $X_i$ is the amount used on trip $i$ and if the trips are independent, then $X_1 + ldots + X_{60}$ has a gamma distribution with $alpha=60$ and rate $1/8$. The function
qgammain R can be used to complete the computation. See math.stackexchange.com/q/2383885 for clarification on the rate vs scale parametrization.$endgroup$
– Just_to_Answer
Jan 9 at 4:18