Answer
(a) P(x=4)=9/25
(b) P(x≤1)=4/25
(c) P(2≤x<4)=12/25
(d) P(x>-10)=1
Work Step by Step
Given that,
f(0)=((2(0)+1)/(25))=(1/(25)),
f(1)=((2(1)+1)/(25))=(3/(25)),
f(2)=((2(2)+1)/(25))=(5/(25)),
f(3)=((2(3)+1)/(25))=(7/(25)),
f(4)=((2(4)+1)/(25))=(9/(25)),
this means that for all possible values of x,
f(x) ≥ 0,
and, P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)=(1/(25))+(3/(25))+(5/(25))+(7/(25))+(9/(25))=((25)/(25))=1
(a) P(x=4)=((2(4)+1)/(25))=(9/(25))
(b) P(x≤1)=P(X=0)+P(X=1)=(1/(25))+(3/(25))=(4/(25))
(c) P(2≤x<4)=P(X=2)+P(X=3)=(5/(25))+(7/(25))==((12)/(25))
(d) P(x>-10)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)=(1/(25))+(3/(25))+(5/(25))+(7/(25))+(9/(25))=((25)/(25))=1
