Question

http://i.imgur.com/NfNgRl5.png

Can anyone help me to understand this statistics question regarding Cumulative distribution functions?

The answer a) 1, because x < or = 50 covers all random variables assigned probabilities
b) 0.75 make sense to me because X > or eqaul to 40 falls in the 0.75 probability range,
but then c) 0.25 d) 0.25 e) 0 f) 0 do not make sense to me at all? Anyone care to explain or am I just not understanding this stuff at all?

Answer 1

@eliassaab anyway you could help me with this if not sorry for bothering you

Answer 2

\[F(k)=P(X\le k)\]
\[P(a\le X\le b)=P(X\le b)-P(X\le a)=F(b)-F(a)\]
\[F(x)=\begin{cases}0&\text{for }x<-10\\
0.25&\text{for }-10\le x<30\\
0.75&\text{for }30\le x<50\\
1&\text{for }x\le50\end{cases}\]
\[(a)~~~~P(X\le50)=F(50)=1\]
\[(b)~~~~P(X\le40)=F(40)=0.75\]
\[(c)~~~~P(40\le X\le60)=F(60)-F(40)=1-0.75=0.25\]
\[(d)~~~~P(X<0)=F(0)=0.25\]
\[(e)~~~~P(0\le X<10)=F(10)-F(0)=0.25-0.25=0\]
\[(f)~~~~P(-10< X<10)=F(10)-F(-10)=0.25-0.25=0\]