Register to reply

Cdf of a discrete random variable and convergence of distributions...

Share this thread:
Artusartos
#1
Jan26-13, 03:28 PM
P: 247
In the page that I attached, it says "...while at the continuity points x of [itex]F_x[/itex] (i.e., [itex]x \not= 0[/itex]), [itex]lim F_{X_n}(x) = F_X(x)[/itex]." But we know that the graph of [itex]F_X(x)[/itex] is a straight line y=0, with only x=0 at y=1, right? But then all the points to the right of zero should not be equal to the limit of [itex]F_{X_n}(x)[/itex], right? Because [itex]F_X(x)[/itex] is always zero at those points, but [itex]F_X(x)[/itex] is 1? So how do I make sense of that?

Thanks in advance
Attached Thumbnails
295(1).jpg  
Phys.Org News Partner Science news on Phys.org
Hoverbike drone project for air transport takes off
Earlier Stone Age artifacts found in Northern Cape of South Africa
Study reveals new characteristics of complex oxide surfaces
Stephen Tashi
#2
Jan27-13, 10:58 AM
Sci Advisor
P: 3,248
Quote Quote by Artusartos View Post
But we know that the graph of [itex]F_X(x)[/itex] is a straight line y=0, with only x=0 at y=1, right?
No, I think [itex] F_X(x) [/itex] is the cumulative distribution, not a density function.
Artusartos
#3
Jan27-13, 11:04 AM
P: 247
Quote Quote by Stephen Tashi View Post
No, I think [itex] F_X(x) [/itex] is the cumulative distribution, not a density function.
Oh, ok...

But it's still confusing. What if n=4 (for example)? Then [tex]F_{X_n} = 1[/tex] if [tex]x \geq 1/4[/tex], and [tex]F_{X_n}=0[/tex], when [tex]x < 1/4[/tex], right? So for any x between 0 and 1/4, the limit at those points is 0, but the limit of [tex]F_X[/tex] at those points is 1...so the limits are not equal, are they?

Stephen Tashi
#4
Jan27-13, 07:23 PM
Sci Advisor
P: 3,248
Cdf of a discrete random variable and convergence of distributions...

Quote Quote by Artusartos View Post
So for any x between 0 and 1/4, the limit at those points is 0,
What limit are you talking about? Something like [itex] lim_{x \rightarrow 1/8} F_{X_4}(x) [/itex] ? I see nothing in the discussion in the book that dealt with that sort of limit. The limits under consideration involve [itex] n \rightarrow \infty [/itex].


Register to reply

Related Discussions
Discrete Random Variable Calculus & Beyond Homework 9
Discrete random variable Precalculus Mathematics Homework 6
Discrete Random Variables and Probability Distributions Calculus & Beyond Homework 10
Logarithm of a discrete random variable Set Theory, Logic, Probability, Statistics 37