Answer
a)$p(X=1)=\frac{1}{2}$
b)$p(X=4)=\frac{1}{16}$
c)$p(X=8)=\frac{1}{256}$
d)$p(X\leq2)=\frac{3}{4}$
e)$p(X\gt 2)=\frac{1}{4}$
Work Step by Step
the probability math function is:
$p(x=x)=0.5\times 0.5^{x-1}=0.5^x, x=1,2,...$
a)$p(X=1)=0.5$
b)$p(X=4)=0.0625=\frac{1}{16}$
c)$p(X=8)=0.00390625=\frac{1}{256}$
d)$p(X\leq2)=p(X=1)+p(X=2)=0.75=\frac{3}{4}$
e)$p(X\gt 2)=1-p(X\leq2)=1-((p(X=1)+p(X=2))=1-0.75=0.25=\frac{1}{4}$
