How to calculate the probability in the following problem?
$begingroup$
Let us consider $f(x)=202+37x+243x^2+a_3x^3$$pmod{257}$, where $a_3$ is randomly chosen from $Bbb{Z}_{257}$. I want to calculate all such $S={f(1),f(2),dots, f(n)}, n<255$ such that $f(t)leq 255$ for all $t=1,2,dots, n$. If $f(t)>255$ for some $t$, then we regerate $a_3$ and this process will continue untill all $f(t)leq 255$. Then what is the probability $Pr(f(t)=r)=?$, $0leq r<257$.
Is my following approach true?
Let $X$ be a random variable in $Bbb{Z}_{256}$, then
$Pr(X=rpmod{256})=Pr(X=0pmod{257})Pr(X=0pmod{256})+Pr(X=1pmod{257})Pr(X=1pmod{256})+Pr(Xneq 0,256pmod{257})Pr(Xneq 0,256pmod{256})$?
I am not sure the above approach true or not.
probability polynomials integers
asked Jan 8 at 3:29
MKSMKS
62
$endgroup$
add a comment |
$begingroup$
Let us consider $f(x)=202+37x+243x^2+a_3x^3$$pmod{257}$, where $a_3$ is randomly chosen from $Bbb{Z}_{257}$. I want to calculate all such $S={f(1),f(2),dots, f(n)}, n<255$ such that $f(t)leq 255$ for all $t=1,2,dots, n$. If $f(t)>255$ for some $t$, then we regerate $a_3$ and this process will continue untill all $f(t)leq 255$. Then what is the probability $Pr(f(t)=r)=?$, $0leq r<257$.
Is my following approach true?
Let $X$ be a random variable in $Bbb{Z}_{256}$, then
$Pr(X=rpmod{256})=Pr(X=0pmod{257})Pr(X=0pmod{256})+Pr(X=1pmod{257})Pr(X=1pmod{256})+Pr(Xneq 0,256pmod{257})Pr(Xneq 0,256pmod{256})$?
I am not sure the above approach true or not.
probability polynomials integers
asked Jan 8 at 3:29
MKSMKS
62
$endgroup$
add a comment |
$begingroup$
Let us consider $f(x)=202+37x+243x^2+a_3x^3$$pmod{257}$, where $a_3$ is randomly chosen from $Bbb{Z}_{257}$. I want to calculate all such $S={f(1),f(2),dots, f(n)}, n<255$ such that $f(t)leq 255$ for all $t=1,2,dots, n$. If $f(t)>255$ for some $t$, then we regerate $a_3$ and this process will continue untill all $f(t)leq 255$. Then what is the probability $Pr(f(t)=r)=?$, $0leq r<257$.
Is my following approach true?
Let $X$ be a random variable in $Bbb{Z}_{256}$, then
$Pr(X=rpmod{256})=Pr(X=0pmod{257})Pr(X=0pmod{256})+Pr(X=1pmod{257})Pr(X=1pmod{256})+Pr(Xneq 0,256pmod{257})Pr(Xneq 0,256pmod{256})$?
I am not sure the above approach true or not.
probability polynomials integers
asked Jan 8 at 3:29
MKSMKS
62
$endgroup$
Let us consider $f(x)=202+37x+243x^2+a_3x^3$$pmod{257}$, where $a_3$ is randomly chosen from $Bbb{Z}_{257}$. I want to calculate all such $S={f(1),f(2),dots, f(n)}, n<255$ such that $f(t)leq 255$ for all $t=1,2,dots, n$. If $f(t)>255$ for some $t$, then we regerate $a_3$ and this process will continue untill all $f(t)leq 255$. Then what is the probability $Pr(f(t)=r)=?$, $0leq r<257$.
Is my following approach true?
Let $X$ be a random variable in $Bbb{Z}_{256}$, then
$Pr(X=rpmod{256})=Pr(X=0pmod{257})Pr(X=0pmod{256})+Pr(X=1pmod{257})Pr(X=1pmod{256})+Pr(Xneq 0,256pmod{257})Pr(Xneq 0,256pmod{256})$?
I am not sure the above approach true or not.
probability polynomials integers
probability polynomials integers
asked Jan 8 at 3:29
MKSMKS
62
asked Jan 8 at 3:29
MKSMKS
62
edited Jan 8 at 3:35
MKS
asked Jan 8 at 3:29
MKSMKS
62
asked Jan 8 at 3:29
MKSMKS
62
asked Jan 8 at 3:29
MKSMKS
62
62
add a comment |
add a comment |
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