Answer
(a) P(X≤1)=4/7
(b) P(X>1)=3/7
(c) P(21)=1
Work Step by Step
Given that,
$f(1)=(8/7)(1/2)^{1}$=4/7,
$f(2)=(8/7)(1/2)^{2}$=2/7,
$f(2)=(8/7)(1/2)^{3}$=1/7,
this means that for all possible values of x,
f(x) ≥ 0,
and, P(X=1)+P(X=2)+P(X=3)=4/7+2/7+1/7=1
(a) P(X≤1)=P(X=1)=4/7
(b) P(X>1)=P(X=2)+P(X=3)=2/7+1/7=3/7
(c) P(21)= P(X=1)+P(X=2)+P(X=3)=4/7+2/7+1/7=1
