- #1
tomtom690
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Homework Statement
I have been given the distribution function F_X of the random variable X and I am asked to find the distribution function F_Y of Y, another random variable which is defined from X in the following way.
Y={[tex]\stackrel{X^{2} if X<2;}{4 if 2\leq X < 3;}\stackrel{4(4-X) if 3\leq X < 4;}{0 if X\geq 4}[/tex]
The distribution function of X is the following:
F_X (x)={[tex]\stackrel{0 if x<1;}{\frac{x+1}{10} if 1 \leq x < \frac{3}{2};}\stackrel{\frac{1}{3}(x-\frac{1}{2}) if \frac{3}{2} \leq x < \frac{5}{2};}{1 if \frac{5}{2} \leq x}[/tex]
I really have very little idea of how to start this, so any pointers at all would be brilliant. I have done a similar question to this before, but then did not start with the distribution, but rather the probability mass function. And we had to find something different at the end as well.
Homework Equations
The Attempt at a Solution
As I said, I'm not entirely sure.
Something has to be done to change it into P_X I think. But I don't know how to do this.
Or should I differentiate F to get f, the density function?
But then what do I do?
Any help would be greatly appreciated.
Many thanks in advance.
After having previewed the post, it is clear that the stacking brackets thing hasn't worked. Please read it as Y having 4 conditions, and the F_X also having 4 conditions. I hope this is clear. The symbols for the imaginary i and the function f together should in fact simply read "if" ie Y= X^2 if X<2.