Answer
a)$p(X=1)=0.4$
b)$p(X=4)=0.0864$
c)$p(X=5)=0.05184$
d)$p(X\leq3)=0.784$
e)$p(X\gt 3)=0.216$
Work Step by Step
X has a geometric distribution with a mean of 2.5, so we can get p as follows:
$p=\frac{1}{\mu}=\frac{1}{2.5}=0.4$
the probability math function is:
$p(x=x)=0.4\times 0.6^{x-1}, x=1,2,...$
a)$p(X=1)=0.4$
b)$p(X=4)=0.0864$
c)$p(X=5)=0.05184$
d)$p(X\leq3)=p(X=1)+p(X=2)+p(X=3)=0.784$
e)$p(X\gt 3)=1-p(X\leq3)=1-0.784=0.216$
