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How to find a constant of a PDF if integral diverges
$begingroup$
So I'm given a probability density function:
p(x) = $frac{ke^{frac{x}{a}}}{a}$ when 0 < x < $infty$
Find the value of k.
I assume I can solve this by solving the equation:
$$int_{0}^{infty} frac{ke^{frac{x}{a}}}{a} dx = 1$$.
However when I solve it find out the integral diverges into infinity.
Even when I use an integral calculator online it gives me the same answer.
Any ideas?
probability integration
asked Jan 27 at 18:01
David MasonDavid Mason
587
$endgroup$
add a comment |
$begingroup$
So I'm given a probability density function:
p(x) = $frac{ke^{frac{x}{a}}}{a}$ when 0 < x < $infty$
Find the value of k.
I assume I can solve this by solving the equation:
$$int_{0}^{infty} frac{ke^{frac{x}{a}}}{a} dx = 1$$.
However when I solve it find out the integral diverges into infinity.
Even when I use an integral calculator online it gives me the same answer.
Any ideas?
probability integration
asked Jan 27 at 18:01
David MasonDavid Mason
587
$endgroup$
1
$begingroup$
Consider what values of $a$ would cause the integral to converge. Also please share what antiderivative you arrived at; your error might be there.
$endgroup$
– Chase Ryan Taylor
Jan 27 at 18:03
add a comment |
$begingroup$
So I'm given a probability density function:
p(x) = $frac{ke^{frac{x}{a}}}{a}$ when 0 < x < $infty$
Find the value of k.
I assume I can solve this by solving the equation:
$$int_{0}^{infty} frac{ke^{frac{x}{a}}}{a} dx = 1$$.
However when I solve it find out the integral diverges into infinity.
Even when I use an integral calculator online it gives me the same answer.
Any ideas?
probability integration
asked Jan 27 at 18:01
David MasonDavid Mason
587
$endgroup$
So I'm given a probability density function:
p(x) = $frac{ke^{frac{x}{a}}}{a}$ when 0 < x < $infty$
Find the value of k.
I assume I can solve this by solving the equation:
$$int_{0}^{infty} frac{ke^{frac{x}{a}}}{a} dx = 1$$.
However when I solve it find out the integral diverges into infinity.
Even when I use an integral calculator online it gives me the same answer.
Any ideas?
probability integration
probability integration
asked Jan 27 at 18:01
David MasonDavid Mason
587
asked Jan 27 at 18:01
David MasonDavid Mason
587
asked Jan 27 at 18:01
David MasonDavid Mason
587
asked Jan 27 at 18:01
David MasonDavid Mason
587
asked Jan 27 at 18:01
David MasonDavid Mason
587
587
1
$begingroup$
Consider what values of $a$ would cause the integral to converge. Also please share what antiderivative you arrived at; your error might be there.
$endgroup$
– Chase Ryan Taylor
Jan 27 at 18:03
add a comment |
1
$begingroup$
Consider what values of $a$ would cause the integral to converge. Also please share what antiderivative you arrived at; your error might be there.
$endgroup$
– Chase Ryan Taylor
Jan 27 at 18:03
1
1
$begingroup$
Consider what values of $a$ would cause the integral to converge. Also please share what antiderivative you arrived at; your error might be there.
$endgroup$
– Chase Ryan Taylor
Jan 27 at 18:03
$begingroup$
Consider what values of $a$ would cause the integral to converge. Also please share what antiderivative you arrived at; your error might be there.
$endgroup$
– Chase Ryan Taylor
Jan 27 at 18:03
add a comment |
0
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$begingroup$
Consider what values of $a$ would cause the integral to converge. Also please share what antiderivative you arrived at; your error might be there.
$endgroup$
– Chase Ryan Taylor
Jan 27 at 18:03