- #1
Roni1985
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- 0
Homework Statement
1. For a random variable X, the function F defined by
F(x) = P(X <= x),−inf < x < inf
is called the cumulative distribution function of X. A property of every distribution function F is that
it is right continuous with left limits.
For the following functions, determine if they are right continuous and/or have left limits at the
indicated values. (A “yes” or “no” answer is insufficient. Justify your answers or no credit will be
given.)
(a) at x = 0 and x = 1 for G(x) = |x|/x .
(b) at x = 0 and x = 1 for H(x) = arctan(x).
Homework Equations
(a) at x = 0 and x = 1 for G(x) = |x|/x .
(b) at x = 0 and x = 1 for H(x) = arctan(x).
The Attempt at a Solution
Well, if we look at 'a', I was trying to find the limit when x->0+ and limit when x->0-. I am getting -1 and 1
but the function is not defined at x=0.
and it's not right continuous nor left continuous, and it has right and left limits, correct?
OR I don't get the question.
Can somebody tell me what I need to do here or lead me to the correct way ??
Thanks in advance,
Roni.