- #1
kasse
- 384
- 1
X is continuously distributed with probability density
[tex]f_{X}(x) = nx^{n-1}, if 0 < x \leq 1[/tex]
and
[tex]f_{X}(x) = 0, otherwise[/tex]
Find the distribution function F(x) of X. Find the probability that X lies between 0.25 and 0.75 when n=1 and when n=2. Find the median of X, i.e. the value of a so that [tex]P(X \leq a) = 1/2[/tex], when n=1 and when n=2. Find E(X) when n=1 and when n=2 and compare with the corresponding medians.
I'm first going to try to find the distribution function. Does this simply mean finding n in the probability density?
[tex]f_{X}(x) = nx^{n-1}, if 0 < x \leq 1[/tex]
and
[tex]f_{X}(x) = 0, otherwise[/tex]
Find the distribution function F(x) of X. Find the probability that X lies between 0.25 and 0.75 when n=1 and when n=2. Find the median of X, i.e. the value of a so that [tex]P(X \leq a) = 1/2[/tex], when n=1 and when n=2. Find E(X) when n=1 and when n=2 and compare with the corresponding medians.
I'm first going to try to find the distribution function. Does this simply mean finding n in the probability density?