How to find p(Y|X), if Y=X+Z and I know the distribution of Z?Marginal DistributionChi Squared Distribution...
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How to find p(Y|X), if Y=X+Z and I know the distribution of Z?
Marginal DistributionChi Squared Distribution with $mu = 0$, $sigma^2 neq 1$Let $X_1$ and $X_2$ are independent $N(0, sigma^2)$ random variables. What is the distribution of $X_1^2 + X_2^2$?Find the distribution of $X_1^2 + X_2^2$?What is the magnitude of Complex random variable Gaussian Case?Find the Distribution of the following;Distribution name and PDFIf $X$ and $Y$ are two NON independent random normal variables, what is the distribution of $Z = frac{X}{Y^n}$Show that the random variables have the same distributionMean and variance of uniform distribution where maximum depends on product of RVs with uniform and Bernoulli
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Suppose I have three random variables $x,y,z$ and they have a relation as
$y=x+z$ now I have the distribution of $z sim p(z)$, how to find $p(y|x)$.
I know intuitively if I have $zsim N(0,sigma^2)$ then $x$ will just impact its mean and so $p(y|x)sim N(x,sigma^2)$.
But I want to know general mathematical procedures to find $p(y|x)$, specifically, if $zsim p(z)$ where $p(z)$ have an undefined MGF and mean and variance both are infinite. Further, I assume that $x$ and $z$ are independent of one another.
probability-theory statistics probability-distributions
asked yesterday
AnkitAnkit
1829
$endgroup$
add a comment |
$begingroup$
Suppose I have three random variables $x,y,z$ and they have a relation as
$y=x+z$ now I have the distribution of $z sim p(z)$, how to find $p(y|x)$.
I know intuitively if I have $zsim N(0,sigma^2)$ then $x$ will just impact its mean and so $p(y|x)sim N(x,sigma^2)$.
But I want to know general mathematical procedures to find $p(y|x)$, specifically, if $zsim p(z)$ where $p(z)$ have an undefined MGF and mean and variance both are infinite. Further, I assume that $x$ and $z$ are independent of one another.
probability-theory statistics probability-distributions
asked yesterday
AnkitAnkit
1829
$endgroup$
1
$begingroup$
@Kavi Rama Murthy I assume $x$ and $z$ are independent of one another.
$endgroup$
– Ankit
yesterday
add a comment |
$begingroup$
Suppose I have three random variables $x,y,z$ and they have a relation as
$y=x+z$ now I have the distribution of $z sim p(z)$, how to find $p(y|x)$.
I know intuitively if I have $zsim N(0,sigma^2)$ then $x$ will just impact its mean and so $p(y|x)sim N(x,sigma^2)$.
But I want to know general mathematical procedures to find $p(y|x)$, specifically, if $zsim p(z)$ where $p(z)$ have an undefined MGF and mean and variance both are infinite. Further, I assume that $x$ and $z$ are independent of one another.
probability-theory statistics probability-distributions
asked yesterday
AnkitAnkit
1829
$endgroup$
Suppose I have three random variables $x,y,z$ and they have a relation as
$y=x+z$ now I have the distribution of $z sim p(z)$, how to find $p(y|x)$.
I know intuitively if I have $zsim N(0,sigma^2)$ then $x$ will just impact its mean and so $p(y|x)sim N(x,sigma^2)$.
But I want to know general mathematical procedures to find $p(y|x)$, specifically, if $zsim p(z)$ where $p(z)$ have an undefined MGF and mean and variance both are infinite. Further, I assume that $x$ and $z$ are independent of one another.
probability-theory statistics probability-distributions
probability-theory statistics probability-distributions
asked yesterday
AnkitAnkit
1829
asked yesterday
AnkitAnkit
1829
edited yesterday
Ankit
asked yesterday
AnkitAnkit
1829
asked yesterday
AnkitAnkit
1829
asked yesterday
AnkitAnkit
1829
1829
1
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@Kavi Rama Murthy I assume $x$ and $z$ are independent of one another.
$endgroup$
– Ankit
yesterday
add a comment |
1
$begingroup$
@Kavi Rama Murthy I assume $x$ and $z$ are independent of one another.
$endgroup$
– Ankit
yesterday
1
1
$begingroup$
@Kavi Rama Murthy I assume $x$ and $z$ are independent of one another.
$endgroup$
– Ankit
yesterday
$begingroup$
@Kavi Rama Murthy I assume $x$ and $z$ are independent of one another.
$endgroup$
– Ankit
yesterday
add a comment |
1 Answer
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The distribution function of $Y$ given $X$ is $F_Z(y-X)$ and the density function is $f_Z(y-X)$ where $F_Z$ and $f_Z$ are the disrtibution function and the density of $Z$ respectively.
answered yesterday
Kavi Rama MurthyKavi Rama Murthy
65.8k42767
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1 Answer
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1 Answer
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$begingroup$
The distribution function of $Y$ given $X$ is $F_Z(y-X)$ and the density function is $f_Z(y-X)$ where $F_Z$ and $f_Z$ are the disrtibution function and the density of $Z$ respectively.
answered yesterday
Kavi Rama MurthyKavi Rama Murthy
65.8k42767
$endgroup$
add a comment |
$begingroup$
The distribution function of $Y$ given $X$ is $F_Z(y-X)$ and the density function is $f_Z(y-X)$ where $F_Z$ and $f_Z$ are the disrtibution function and the density of $Z$ respectively.
answered yesterday
Kavi Rama MurthyKavi Rama Murthy
65.8k42767
$endgroup$
add a comment |
$begingroup$
The distribution function of $Y$ given $X$ is $F_Z(y-X)$ and the density function is $f_Z(y-X)$ where $F_Z$ and $f_Z$ are the disrtibution function and the density of $Z$ respectively.
answered yesterday
Kavi Rama MurthyKavi Rama Murthy
65.8k42767
$endgroup$
The distribution function of $Y$ given $X$ is $F_Z(y-X)$ and the density function is $f_Z(y-X)$ where $F_Z$ and $f_Z$ are the disrtibution function and the density of $Z$ respectively.
answered yesterday
Kavi Rama MurthyKavi Rama Murthy
65.8k42767
answered yesterday
Kavi Rama MurthyKavi Rama Murthy
65.8k42767
answered yesterday
Kavi Rama MurthyKavi Rama Murthy
65.8k42767
answered yesterday
Kavi Rama MurthyKavi Rama Murthy
65.8k42767
65.8k42767
add a comment |
add a comment |
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@Kavi Rama Murthy I assume $x$ and $z$ are independent of one another.
$endgroup$
– Ankit
yesterday