Answer
(a) P(X≤2)=1
(b)P(X>-2)=0.8
(c) P(-1$\leq$X$\leq1)$=0.7
(d) P(X ≤-1 or X=2)=0.7
Work Step by Step
Given that,
$f( -2)=0.2, f( -1)=0.4,f( 0)=0.1,f( 1)=0.2,f( 2)=0.1,$
this means that for all possible values of x,
f(x) ≥ 0,
and, P(X=-2)+P(X=-1)+P(X=0)+P(X=1)+P(X=2)=0.2+0.4+0.1+0.2+0.1=1
(a) P(X≤2)=P(X=-2)+P(X=-1)+P(X=0)+P(X=1)+P(X=2)
=0.2+0.4+0.1+0.2+0.1=1
(b)P(X>-2)=P(X=-1)+P(X=0)+P(X=1)+P(X=2)=0.4+0.1+0.2+0.1=0.8
(c) P(-1$\leq$X$\leq1)$=P(X=-1)+P(X=0)+P(X=1)=0.4+0.1+0.2=0.7
(d) P(X ≤-1 or X=2)= P(X=-2)+P(X=-1)+P(X=2)=0.2+0.4+0.1=0.7
