# Thread: cumulative distribution function question

1. ## cumulative distribution function question

consider rolling a die.
S= {1,2,3,4,5,6}
P(s)=1/6 for all s in S
X= number on die so that X(s)=s for all s in S
Y= X^2
compute the cumulative distribution function Fy(y) = P(Y<=y), for all y in the set of real numbers.

My guess
for Y=1 i get
P(-inf<y<=1)=P(Y<=1)-P(Y<-inf)=Fx(1)-Fx(-inf)
= Fx(1)-0
= Fx(1)

Is this all I have to do for Y=1, or do I have to integrate, or is there anything wrong?

2. you have been told that $Y = X^2$

so,

$F_{Y}(y) = P(Y \leq y) = P(X^2 \leq y)$

continue further to find the cdf of Y....

3. i go further but i am stuck at
1-P(-x<y)-P(y<x)

4. $P(Y \leqslant x) = F_Y(x) = \left\{ {\begin{array}{rl}
{0,} & {x < 1} \\
{\frac{1}
{6},} & {1 \leqslant x < 4} \\
{\frac{2}
{6},} & {4 \leqslant x < 9} \\
{ \vdots ,} & \vdots \\
{1,} & {36 \leqslant x} \\ \end{array} } \right.$

You fill in the blanks.

5. ok i understand now.