Support of Beta Random Variable Times Constant and then Floored
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Let $Xsim Beta(alpha, beta)$ and let $ninmathbbZ^+$. Define the new random variable
$$Y=lfloor nXrfloor$$
What is the support of $Y$? Is it $0,1,...,n-1$ or is it $0,1,...,n$?
I'm sort of confused by this question, because I have seen the Beta distribution being defined in two ways; with support $(0, 1)$ as well as with support $[0,1]$. But even if its support is $[0,1]$, technically $P(X=1)=0$. So is it always true that $Y$ has support $0,1,...,n-1$?
probability probability-theory probability-distributions random-variables
asked Sep 2 at 6:07
jippyjoe4
4247
add a comment |Â
up vote
0
down vote
favorite
Let $Xsim Beta(alpha, beta)$ and let $ninmathbbZ^+$. Define the new random variable
$$Y=lfloor nXrfloor$$
What is the support of $Y$? Is it $0,1,...,n-1$ or is it $0,1,...,n$?
I'm sort of confused by this question, because I have seen the Beta distribution being defined in two ways; with support $(0, 1)$ as well as with support $[0,1]$. But even if its support is $[0,1]$, technically $P(X=1)=0$. So is it always true that $Y$ has support $0,1,...,n-1$?
probability probability-theory probability-distributions random-variables
asked Sep 2 at 6:07
jippyjoe4
4247
2
"So it it always true that " - Yes.
– zhoraster
Sep 2 at 6:48
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let $Xsim Beta(alpha, beta)$ and let $ninmathbbZ^+$. Define the new random variable
$$Y=lfloor nXrfloor$$
What is the support of $Y$? Is it $0,1,...,n-1$ or is it $0,1,...,n$?
I'm sort of confused by this question, because I have seen the Beta distribution being defined in two ways; with support $(0, 1)$ as well as with support $[0,1]$. But even if its support is $[0,1]$, technically $P(X=1)=0$. So is it always true that $Y$ has support $0,1,...,n-1$?
probability probability-theory probability-distributions random-variables
asked Sep 2 at 6:07
jippyjoe4
4247
Let $Xsim Beta(alpha, beta)$ and let $ninmathbbZ^+$. Define the new random variable
$$Y=lfloor nXrfloor$$
What is the support of $Y$? Is it $0,1,...,n-1$ or is it $0,1,...,n$?
I'm sort of confused by this question, because I have seen the Beta distribution being defined in two ways; with support $(0, 1)$ as well as with support $[0,1]$. But even if its support is $[0,1]$, technically $P(X=1)=0$. So is it always true that $Y$ has support $0,1,...,n-1$?
probability probability-theory probability-distributions random-variables
probability probability-theory probability-distributions random-variables
asked Sep 2 at 6:07
jippyjoe4
4247
asked Sep 2 at 6:07
jippyjoe4
4247
edited Sep 2 at 21:20
asked Sep 2 at 6:07
jippyjoe4
4247
asked Sep 2 at 6:07
jippyjoe4
4247
asked Sep 2 at 6:07
jippyjoe4
4247
4247
2
"So it it always true that " - Yes.
– zhoraster
Sep 2 at 6:48
add a comment |Â
2
"So it it always true that " - Yes.
– zhoraster
Sep 2 at 6:48
2
2
"So it it always true that " - Yes.
– zhoraster
Sep 2 at 6:48
"So it it always true that " - Yes.
– zhoraster
Sep 2 at 6:48
add a comment |Â
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2
"So it it always true that " - Yes.
– zhoraster
Sep 2 at 6:48