Probability Density Function Notation
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So Im new to pdf's and am doing some preliminary research on the topic. I came across notation that I didn't understand. The problem I found said this:
A random variable I has the following PDF:
$P_i(i) = frac{4i}{a^2} U(i)$
where the variable i is simple the value of the random variable I.
Determine the PDF of the new random variable:
$X = frac{1}{I}$
using the following approaches:
a) the direct technique, i.e.,
calculating the Jacobian of the inverse transformation, etc., and b)
by first determining the CDF of the new RV, X, and then
differentiating.
In the notation above, what does the U(i) mean. Is it specifying a uniform distribution?
probability density-function
asked Dec 8 '18 at 5:05
crazyCodercrazyCoder
1012
$endgroup$
add a comment |
$begingroup$
So Im new to pdf's and am doing some preliminary research on the topic. I came across notation that I didn't understand. The problem I found said this:
A random variable I has the following PDF:
$P_i(i) = frac{4i}{a^2} U(i)$
where the variable i is simple the value of the random variable I.
Determine the PDF of the new random variable:
$X = frac{1}{I}$
using the following approaches:
a) the direct technique, i.e.,
calculating the Jacobian of the inverse transformation, etc., and b)
by first determining the CDF of the new RV, X, and then
differentiating.
In the notation above, what does the U(i) mean. Is it specifying a uniform distribution?
probability density-function
asked Dec 8 '18 at 5:05
crazyCodercrazyCoder
1012
$endgroup$
$begingroup$
Can you supply the reference to that problem?
$endgroup$
– JimB
Dec 8 '18 at 5:16
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@JimB I've updated the question to show the full question that was asked. It's just a random problem from a probability textbook
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– crazyCoder
Dec 8 '18 at 5:25
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Not all spaces have uniform distributions. In particular, any unbounded subset of $Bbb R$ does not. So unless $I$ is restricted to some bounded range, $U(i)$ cannot be a uniform distribution. You need to search the context of this problem in the textbook to figure out what $U(i)$ is supposed to be.
$endgroup$
– Paul Sinclair
Dec 8 '18 at 14:40
add a comment |
$begingroup$
So Im new to pdf's and am doing some preliminary research on the topic. I came across notation that I didn't understand. The problem I found said this:
A random variable I has the following PDF:
$P_i(i) = frac{4i}{a^2} U(i)$
where the variable i is simple the value of the random variable I.
Determine the PDF of the new random variable:
$X = frac{1}{I}$
using the following approaches:
a) the direct technique, i.e.,
calculating the Jacobian of the inverse transformation, etc., and b)
by first determining the CDF of the new RV, X, and then
differentiating.
In the notation above, what does the U(i) mean. Is it specifying a uniform distribution?
probability density-function
asked Dec 8 '18 at 5:05
crazyCodercrazyCoder
1012
$endgroup$
So Im new to pdf's and am doing some preliminary research on the topic. I came across notation that I didn't understand. The problem I found said this:
A random variable I has the following PDF:
$P_i(i) = frac{4i}{a^2} U(i)$
where the variable i is simple the value of the random variable I.
Determine the PDF of the new random variable:
$X = frac{1}{I}$
using the following approaches:
a) the direct technique, i.e.,
calculating the Jacobian of the inverse transformation, etc., and b)
by first determining the CDF of the new RV, X, and then
differentiating.
In the notation above, what does the U(i) mean. Is it specifying a uniform distribution?
probability density-function
probability density-function
asked Dec 8 '18 at 5:05
crazyCodercrazyCoder
1012
asked Dec 8 '18 at 5:05
crazyCodercrazyCoder
1012
edited Dec 8 '18 at 5:30
crazyCoder
asked Dec 8 '18 at 5:05
crazyCodercrazyCoder
1012
asked Dec 8 '18 at 5:05
crazyCodercrazyCoder
1012
asked Dec 8 '18 at 5:05
crazyCodercrazyCoder
1012
1012
$begingroup$
Can you supply the reference to that problem?
$endgroup$
– JimB
Dec 8 '18 at 5:16
$begingroup$
@JimB I've updated the question to show the full question that was asked. It's just a random problem from a probability textbook
$endgroup$
– crazyCoder
Dec 8 '18 at 5:25
$begingroup$
Not all spaces have uniform distributions. In particular, any unbounded subset of $Bbb R$ does not. So unless $I$ is restricted to some bounded range, $U(i)$ cannot be a uniform distribution. You need to search the context of this problem in the textbook to figure out what $U(i)$ is supposed to be.
$endgroup$
– Paul Sinclair
Dec 8 '18 at 14:40
add a comment |
$begingroup$
Can you supply the reference to that problem?
$endgroup$
– JimB
Dec 8 '18 at 5:16
$begingroup$
@JimB I've updated the question to show the full question that was asked. It's just a random problem from a probability textbook
$endgroup$
– crazyCoder
Dec 8 '18 at 5:25
$begingroup$
Not all spaces have uniform distributions. In particular, any unbounded subset of $Bbb R$ does not. So unless $I$ is restricted to some bounded range, $U(i)$ cannot be a uniform distribution. You need to search the context of this problem in the textbook to figure out what $U(i)$ is supposed to be.
$endgroup$
– Paul Sinclair
Dec 8 '18 at 14:40
$begingroup$
Can you supply the reference to that problem?
$endgroup$
– JimB
Dec 8 '18 at 5:16
$begingroup$
Can you supply the reference to that problem?
$endgroup$
– JimB
Dec 8 '18 at 5:16
$begingroup$
@JimB I've updated the question to show the full question that was asked. It's just a random problem from a probability textbook
$endgroup$
– crazyCoder
Dec 8 '18 at 5:25
$begingroup$
@JimB I've updated the question to show the full question that was asked. It's just a random problem from a probability textbook
$endgroup$
– crazyCoder
Dec 8 '18 at 5:25
$begingroup$
Not all spaces have uniform distributions. In particular, any unbounded subset of $Bbb R$ does not. So unless $I$ is restricted to some bounded range, $U(i)$ cannot be a uniform distribution. You need to search the context of this problem in the textbook to figure out what $U(i)$ is supposed to be.
$endgroup$
– Paul Sinclair
Dec 8 '18 at 14:40
$begingroup$
Not all spaces have uniform distributions. In particular, any unbounded subset of $Bbb R$ does not. So unless $I$ is restricted to some bounded range, $U(i)$ cannot be a uniform distribution. You need to search the context of this problem in the textbook to figure out what $U(i)$ is supposed to be.
$endgroup$
– Paul Sinclair
Dec 8 '18 at 14:40
add a comment |
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$begingroup$
Can you supply the reference to that problem?
$endgroup$
– JimB
Dec 8 '18 at 5:16
$begingroup$
@JimB I've updated the question to show the full question that was asked. It's just a random problem from a probability textbook
$endgroup$
– crazyCoder
Dec 8 '18 at 5:25
$begingroup$
Not all spaces have uniform distributions. In particular, any unbounded subset of $Bbb R$ does not. So unless $I$ is restricted to some bounded range, $U(i)$ cannot be a uniform distribution. You need to search the context of this problem in the textbook to figure out what $U(i)$ is supposed to be.
$endgroup$
– Paul Sinclair
Dec 8 '18 at 14:40