What will be the pdf of $X+Y$?
Suppose $X$ and $Y$ are independent random variables. Let $f$ and $g$ be the pdf of $X$ and $Y$ respectively. Let $h$ be the pdf of $X+Y$ then can we say that $h(x)=f(x)g(x),$ for all $x in Bbb R$? If so why?
Please help me in this regard. Thank you very much.
probability probability-theory random-variables independence density-function
asked Nov 30 '18 at 18:40
Dbchatto67Dbchatto67
52215
add a comment |
Suppose $X$ and $Y$ are independent random variables. Let $f$ and $g$ be the pdf of $X$ and $Y$ respectively. Let $h$ be the pdf of $X+Y$ then can we say that $h(x)=f(x)g(x),$ for all $x in Bbb R$? If so why?
Please help me in this regard. Thank you very much.
probability probability-theory random-variables independence density-function
asked Nov 30 '18 at 18:40
Dbchatto67Dbchatto67
52215
add a comment |
Suppose $X$ and $Y$ are independent random variables. Let $f$ and $g$ be the pdf of $X$ and $Y$ respectively. Let $h$ be the pdf of $X+Y$ then can we say that $h(x)=f(x)g(x),$ for all $x in Bbb R$? If so why?
Please help me in this regard. Thank you very much.
probability probability-theory random-variables independence density-function
asked Nov 30 '18 at 18:40
Dbchatto67Dbchatto67
52215
Suppose $X$ and $Y$ are independent random variables. Let $f$ and $g$ be the pdf of $X$ and $Y$ respectively. Let $h$ be the pdf of $X+Y$ then can we say that $h(x)=f(x)g(x),$ for all $x in Bbb R$? If so why?
Please help me in this regard. Thank you very much.
probability probability-theory random-variables independence density-function
probability probability-theory random-variables independence density-function
asked Nov 30 '18 at 18:40
Dbchatto67Dbchatto67
52215
asked Nov 30 '18 at 18:40
Dbchatto67Dbchatto67
52215
asked Nov 30 '18 at 18:40
Dbchatto67Dbchatto67
52215
asked Nov 30 '18 at 18:40
Dbchatto67Dbchatto67
52215
asked Nov 30 '18 at 18:40
Dbchatto67Dbchatto67
52215
52215
add a comment |
add a comment |
1 Answer
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It is called convolution
$h(x) = int_{-infty} ^ {infty} f(y) g(x-y) dy $
answered Nov 30 '18 at 18:46
MoonKnightMoonKnight
1,324611
add a comment |
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1 Answer
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1 Answer
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active
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It is called convolution
$h(x) = int_{-infty} ^ {infty} f(y) g(x-y) dy $
answered Nov 30 '18 at 18:46
MoonKnightMoonKnight
1,324611
add a comment |
It is called convolution
$h(x) = int_{-infty} ^ {infty} f(y) g(x-y) dy $
answered Nov 30 '18 at 18:46
MoonKnightMoonKnight
1,324611
add a comment |
It is called convolution
$h(x) = int_{-infty} ^ {infty} f(y) g(x-y) dy $
answered Nov 30 '18 at 18:46
MoonKnightMoonKnight
1,324611
It is called convolution
$h(x) = int_{-infty} ^ {infty} f(y) g(x-y) dy $
answered Nov 30 '18 at 18:46
MoonKnightMoonKnight
1,324611
answered Nov 30 '18 at 18:46
MoonKnightMoonKnight
1,324611
answered Nov 30 '18 at 18:46
MoonKnightMoonKnight
1,324611
answered Nov 30 '18 at 18:46
MoonKnightMoonKnight
1,324611
1,324611
add a comment |
add a comment |
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