Eidos
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Hey guys
I'd like a steer in the right direction with this problem.
I would like to show that
P\{x_1\leq X \leq x_2\}=F_{X}(x_2)-F_{X}(x_1^{-})\quad(1)
Where:
X is a random variable.
F_{X}(x) \equiv P\{X \leq x \} is its cumulative distribution function.
My notes only give an example (using dice) to show that this is true.
Generally
P\{x_1 < X \leq x_2\}=F_{X}(x_2)-F_{X}(x_1)\quad(2)
and
P\{X = x_2\}=F_{X}(x_2)-F_{X}(x_2^{-})\quad (3)
the latter of which is easy to prove.
I've been trying to rewrite (1) in terms of (2) & (3) but have had no success so far.
Any ideas would be most welcomed
I'd like a steer in the right direction with this problem.
I would like to show that
P\{x_1\leq X \leq x_2\}=F_{X}(x_2)-F_{X}(x_1^{-})\quad(1)
Where:
X is a random variable.
F_{X}(x) \equiv P\{X \leq x \} is its cumulative distribution function.
My notes only give an example (using dice) to show that this is true.
Generally
P\{x_1 < X \leq x_2\}=F_{X}(x_2)-F_{X}(x_1)\quad(2)
and
P\{X = x_2\}=F_{X}(x_2)-F_{X}(x_2^{-})\quad (3)
the latter of which is easy to prove.
I've been trying to rewrite (1) in terms of (2) & (3) but have had no success so far.
Any ideas would be most welcomed
