What is the Probability density function of $X^2$ where X is an Uniform distribution
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I'm a student and I'm studying random variables and very new to it. I was studying the Uniform distribution and in it, it calculates the Expected of $X^2$ by $$ Eleft(X^2right) = int_{- infty}^infty x^2 p(x) dx $$
I understand the calculation of it, but if the Probability density function plot of $X$ is like that (I fully understand that) I can't imagine the Probability density function of the $X^2$ because if we span the Probability density function of $X$ which is within $[a,b]$ to $[a^2,b^2]$ then the integral of $int_{a^2}^{b^2} p(sqrt x) dx$ may not be equal to 1 I guess.
Could you help me figure out what is the Probability density function of $X^2$?
random-variables uniform-distribution density-function expected-value
edited Dec 31 '18 at 21:15
Davide Giraudo
128k17156268
asked Dec 23 '18 at 17:17
Peyman mohseni kiasariPeyman mohseni kiasari
14911
$endgroup$
add a comment |
$begingroup$
I'm a student and I'm studying random variables and very new to it. I was studying the Uniform distribution and in it, it calculates the Expected of $X^2$ by $$ Eleft(X^2right) = int_{- infty}^infty x^2 p(x) dx $$
I understand the calculation of it, but if the Probability density function plot of $X$ is like that (I fully understand that) I can't imagine the Probability density function of the $X^2$ because if we span the Probability density function of $X$ which is within $[a,b]$ to $[a^2,b^2]$ then the integral of $int_{a^2}^{b^2} p(sqrt x) dx$ may not be equal to 1 I guess.
Could you help me figure out what is the Probability density function of $X^2$?
random-variables uniform-distribution density-function expected-value
edited Dec 31 '18 at 21:15
Davide Giraudo
128k17156268
asked Dec 23 '18 at 17:17
Peyman mohseni kiasariPeyman mohseni kiasari
14911
$endgroup$
1
$begingroup$
I actually computed the pdf of $X^2$ for a general random variable here: math.stackexchange.com/a/3043502/90543
$endgroup$
– jgon
Dec 23 '18 at 17:21
$begingroup$
@jgon thank you. it was hard for me to understand your answer because I'm very new to it, but finally, I get it. so I was right, it is not that simple that in the basic tutorials they just integral $int_{- infty}^infty x^2 p(x) d_x $ to find the Expected. nice answer.
$endgroup$
– Peyman mohseni kiasari
Dec 23 '18 at 17:36
add a comment |
$begingroup$
I'm a student and I'm studying random variables and very new to it. I was studying the Uniform distribution and in it, it calculates the Expected of $X^2$ by $$ Eleft(X^2right) = int_{- infty}^infty x^2 p(x) dx $$
I understand the calculation of it, but if the Probability density function plot of $X$ is like that (I fully understand that) I can't imagine the Probability density function of the $X^2$ because if we span the Probability density function of $X$ which is within $[a,b]$ to $[a^2,b^2]$ then the integral of $int_{a^2}^{b^2} p(sqrt x) dx$ may not be equal to 1 I guess.
Could you help me figure out what is the Probability density function of $X^2$?
random-variables uniform-distribution density-function expected-value
edited Dec 31 '18 at 21:15
Davide Giraudo
128k17156268
asked Dec 23 '18 at 17:17
Peyman mohseni kiasariPeyman mohseni kiasari
14911
$endgroup$
I'm a student and I'm studying random variables and very new to it. I was studying the Uniform distribution and in it, it calculates the Expected of $X^2$ by $$ Eleft(X^2right) = int_{- infty}^infty x^2 p(x) dx $$
I understand the calculation of it, but if the Probability density function plot of $X$ is like that (I fully understand that) I can't imagine the Probability density function of the $X^2$ because if we span the Probability density function of $X$ which is within $[a,b]$ to $[a^2,b^2]$ then the integral of $int_{a^2}^{b^2} p(sqrt x) dx$ may not be equal to 1 I guess.
Could you help me figure out what is the Probability density function of $X^2$?
random-variables uniform-distribution density-function expected-value
random-variables uniform-distribution density-function expected-value
edited Dec 31 '18 at 21:15
Davide Giraudo
128k17156268
asked Dec 23 '18 at 17:17
Peyman mohseni kiasariPeyman mohseni kiasari
14911
edited Dec 31 '18 at 21:15
Davide Giraudo
128k17156268
asked Dec 23 '18 at 17:17
Peyman mohseni kiasariPeyman mohseni kiasari
14911
edited Dec 31 '18 at 21:15
Davide Giraudo
128k17156268
edited Dec 31 '18 at 21:15
Davide Giraudo
128k17156268
edited Dec 31 '18 at 21:15
Davide Giraudo
128k17156268
128k17156268
asked Dec 23 '18 at 17:17
Peyman mohseni kiasariPeyman mohseni kiasari
14911
asked Dec 23 '18 at 17:17
Peyman mohseni kiasariPeyman mohseni kiasari
14911
asked Dec 23 '18 at 17:17
Peyman mohseni kiasariPeyman mohseni kiasari
14911
14911
1
$begingroup$
I actually computed the pdf of $X^2$ for a general random variable here: math.stackexchange.com/a/3043502/90543
$endgroup$
– jgon
Dec 23 '18 at 17:21
$begingroup$
@jgon thank you. it was hard for me to understand your answer because I'm very new to it, but finally, I get it. so I was right, it is not that simple that in the basic tutorials they just integral $int_{- infty}^infty x^2 p(x) d_x $ to find the Expected. nice answer.
$endgroup$
– Peyman mohseni kiasari
Dec 23 '18 at 17:36
add a comment |
1
$begingroup$
I actually computed the pdf of $X^2$ for a general random variable here: math.stackexchange.com/a/3043502/90543
$endgroup$
– jgon
Dec 23 '18 at 17:21
$begingroup$
@jgon thank you. it was hard for me to understand your answer because I'm very new to it, but finally, I get it. so I was right, it is not that simple that in the basic tutorials they just integral $int_{- infty}^infty x^2 p(x) d_x $ to find the Expected. nice answer.
$endgroup$
– Peyman mohseni kiasari
Dec 23 '18 at 17:36
1
1
$begingroup$
I actually computed the pdf of $X^2$ for a general random variable here: math.stackexchange.com/a/3043502/90543
$endgroup$
– jgon
Dec 23 '18 at 17:21
$begingroup$
I actually computed the pdf of $X^2$ for a general random variable here: math.stackexchange.com/a/3043502/90543
$endgroup$
– jgon
Dec 23 '18 at 17:21
$begingroup$
@jgon thank you. it was hard for me to understand your answer because I'm very new to it, but finally, I get it. so I was right, it is not that simple that in the basic tutorials they just integral $int_{- infty}^infty x^2 p(x) d_x $ to find the Expected. nice answer.
$endgroup$
– Peyman mohseni kiasari
Dec 23 '18 at 17:36
$begingroup$
@jgon thank you. it was hard for me to understand your answer because I'm very new to it, but finally, I get it. so I was right, it is not that simple that in the basic tutorials they just integral $int_{- infty}^infty x^2 p(x) d_x $ to find the Expected. nice answer.
$endgroup$
– Peyman mohseni kiasari
Dec 23 '18 at 17:36
add a comment |
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$begingroup$
I actually computed the pdf of $X^2$ for a general random variable here: math.stackexchange.com/a/3043502/90543
$endgroup$
– jgon
Dec 23 '18 at 17:21
$begingroup$
@jgon thank you. it was hard for me to understand your answer because I'm very new to it, but finally, I get it. so I was right, it is not that simple that in the basic tutorials they just integral $int_{- infty}^infty x^2 p(x) d_x $ to find the Expected. nice answer.
$endgroup$
– Peyman mohseni kiasari
Dec 23 '18 at 17:36