Dgdrxrt

Cooking pasta in a water boiler

If my opponent casts Ultimate Price on my Phantasmal Bear, can I save it by casting Snap or Curfew?

Correct punctuation for showing a character's confusion

Deal with toxic manager when you can't quit

Match Roman Numerals

Can you cast a spell on someone in the Ethereal Plane, if you are on the Material Plane and have the True Seeing spell active?

How did passengers keep warm on sail ships?

What is the most efficient way to store a numeric range?

Is it ethical to upload a automatically generated paper to a non peer-reviewed site as part of a larger research?

How to charge AirPods to keep battery healthy?

Worn-tile Scrabble

Why not take a picture of a closer black hole?

Finding the area between two curves with Integrate

Can there be female White Walkers?

Short story: child made less intelligent and less attractive

Why couldn't they take pictures of a closer black hole?

Is an up-to-date browser secure on an out-of-date OS?

How to notate time signature switching consistently every measure

Mathematics of imaging the black hole

How can I define good in a religion that claims no moral authority?

Short story: man watches girlfriend's spaceship entering a 'black hole' (?) forever

What to do when moving next to a bird sanctuary with a loosely-domesticated cat?

How to type this arrow in math mode?

Can we generate random numbers using irrational numbers like π and e?

Show that the conditionnal distribution of Y1| $cq(Y1)U1 leq p(Y1)$ is given by the mass function p on $mathbb N$

0

$begingroup$

Let $Z$ be a discrete random variable, and her distribution is given by the function $p$, $p(k) = P [Z = k]$.
Suppose we know how to simulate another discrete random variable $Y$ her distribution is given by the function $q$, $q(k)=P[Y =k]$ and such that we have $ ∃c>1, ∀k∈N, p(k)≤cq(k)$

For the exercise we consider $(Y_n)_n geq 1$ a sequence of random variable i.i.d. with the same distribution than $Y$ and $ (U_n)_n geq 1$
a sequence of random variable i.i.d. uniform on $[0,1]$ and independant from $(Y_n)_n geq 1$.

Let $tau$ = inf $ngeq1, cq(Y_n)U_n ≤ p(Y_n)$ .

I want to show that the conditional distribution of $Y1$| $cq(Y1)U1 leq p(Y1)$ is given by the mass function $p$ on $mathbb N$

probability probability-theory probability-distributions conditional-probability

share|cite|improve this question

edited Mar 31 at 20:58

Farouk Deutsch

asked Mar 30 at 23:27

Farouk DeutschFarouk Deutsch

1239

$endgroup$

add a comment | 

0

$begingroup$

Let $Z$ be a discrete random variable, and her distribution is given by the function $p$, $p(k) = P [Z = k]$.
Suppose we know how to simulate another discrete random variable $Y$ her distribution is given by the function $q$, $q(k)=P[Y =k]$ and such that we have $ ∃c>1, ∀k∈N, p(k)≤cq(k)$

For the exercise we consider $(Y_n)_n geq 1$ a sequence of random variable i.i.d. with the same distribution than $Y$ and $ (U_n)_n geq 1$
a sequence of random variable i.i.d. uniform on $[0,1]$ and independant from $(Y_n)_n geq 1$.

Let $tau$ = inf $ngeq1, cq(Y_n)U_n ≤ p(Y_n)$ .

I want to show that the conditional distribution of $Y1$| $cq(Y1)U1 leq p(Y1)$ is given by the mass function $p$ on $mathbb N$

probability probability-theory probability-distributions conditional-probability

share|cite|improve this question

edited Mar 31 at 20:58

Farouk Deutsch

asked Mar 30 at 23:27

Farouk DeutschFarouk Deutsch

1239

$endgroup$

add a comment | 

$begingroup$

Let $Z$ be a discrete random variable, and her distribution is given by the function $p$, $p(k) = P [Z = k]$.
Suppose we know how to simulate another discrete random variable $Y$ her distribution is given by the function $q$, $q(k)=P[Y =k]$ and such that we have $ ∃c>1, ∀k∈N, p(k)≤cq(k)$

For the exercise we consider $(Y_n)_n geq 1$ a sequence of random variable i.i.d. with the same distribution than $Y$ and $ (U_n)_n geq 1$
a sequence of random variable i.i.d. uniform on $[0,1]$ and independant from $(Y_n)_n geq 1$.

Let $tau$ = inf $ngeq1, cq(Y_n)U_n ≤ p(Y_n)$ .

I want to show that the conditional distribution of $Y1$| $cq(Y1)U1 leq p(Y1)$ is given by the mass function $p$ on $mathbb N$

probability probability-theory probability-distributions conditional-probability

share|cite|improve this question

edited Mar 31 at 20:58

Farouk Deutsch

asked Mar 30 at 23:27

Farouk DeutschFarouk Deutsch

1239

$endgroup$

share|cite|improve this question

edited Mar 31 at 20:58

Farouk Deutsch

asked Mar 30 at 23:27

Farouk DeutschFarouk Deutsch

1239

share|cite|improve this question

edited Mar 31 at 20:58

Farouk Deutsch

asked Mar 30 at 23:27

Farouk DeutschFarouk Deutsch

1239

asked Mar 30 at 23:27

Farouk DeutschFarouk Deutsch

1239

asked Mar 30 at 23:27

Farouk DeutschFarouk Deutsch

1239