David
Reputation
543
Top tag
Next privilege 1,000 Rep.
Create tags
 Jun15 accepted x in the range of a random variable $X$ implies the pdf $f_X(x)>0$ Jun15 comment x in the range of a random variable $X$ implies the pdf $f_X(x)>0$ I am trying to read Casella's Statistical Inference, and up to the page I am on, he had been using $\mathcal X$ as the range of a random variable $X$. Then he says: "When the transformation is from $X$ to $Y=g(X)$, it is most convenient to use $\mathcal X=\{x: f_X(x)>0\}$. The pdf of the random variable $X$ is positive only on the set $\mathcal X$ and is 0 elsewhere. Such a set is called the support set of a distribution or, more informally, the support of a distribution." So it seems like I misunderstood that an adjustment was being made. Jun15 asked x in the range of a random variable $X$ implies the pdf $f_X(x)>0$ Jun13 comment Inverse of partitioned matrix, checking result Very nice move. Jun13 comment Inverse of partitioned matrix, checking result Excellent suggestion, and it worked. Jun13 accepted Inverse of partitioned matrix, checking result Jun13 asked Inverse of partitioned matrix, checking result Jun12 accepted Marginal pdf $f_2(y)$ is proportional to $g_2(y)$. Jun12 comment Marginal pdf $f_2(y)$ is proportional to $g_2(y)$. Very helpful. Thanks. Jun12 asked Marginal pdf $f_2(y)$ is proportional to $g_2(y)$. Jun8 revised If F is a cumulative distribution function, then $\lim_{x\to\infty}F(x)=1$ added 66 characters in body Jun8 comment If F is a cumulative distribution function, then $\lim_{x\to\infty}F(x)=1$ Agree, making a correction. Jun8 asked If F is a cumulative distribution function, then $\lim_{x\to\infty}F(x)=1$ Jun6 comment Transform rectangular region to region bounded by $y=1$ and $y=x^2$ OK, I do see that if you fix $v$ then $u$ varies between $u=-\sqrt v$ and $u=\sqrt v$, but why does that make you pick $x=u\sqrt v$ and $y=v$? Jun6 comment Transform rectangular region to region bounded by $y=1$ and $y=x^2$ This answer appears to be correct. I'm sorry, I'm just not seeing how you did this so quickly and easily. Jun6 comment Transform rectangular region to region bounded by $y=1$ and $y=x^2$ Two questions: 1) How did you figure this out? 2) I don't think it is correct as I believe it maps the region $(-1,1)\times(0,1)$ into the region $(-1,1)\times(0,1)$ minus the region bounded by the curves $y=1$ and $y=x^2$. Jun6 asked Transform rectangular region to region bounded by $y=1$ and $y=x^2$ Jun3 asked The p.d.f as a derivative of the c.d.f. Jun3 accepted What is a bounded discrete random variable Jun3 comment What is a bounded discrete random variable And this means that the normal random variable Z is unbounded?