Chapter 3 - Section 3-7 - Geometric and Negative Binomial Distributions - Exercises - Page 91: 3-123

a) $f(X=4) = 0.0064$ b) $f(X\leq4) = 0.9984$ c) $f(X\geq4) = 0.008$

We have a geometric random variable, so the basic type is: $f(x)=(1-p)^{x-1}\times p$ a) $f(X=4)=(1-0.8)^{4-1}\times 0.8= 0.0064$ b)$f(X\leq4)= f(X=1) + f(X=2) + f(X=3) + f(X=4)= 0.8+0.16+0.032+0.0064= 0.9984$ c) $f(X\geq4) = 1-f(X\leq4) = 1- f(X=1) - f(X=2) - f(X=3) = 0.008$