Answer
$$F(x)=\left\{\begin{array}{ll}{0} & {x<0} \\ {0.125} & {0 \leq x<1} \\ {0.5} & {1 \leq x<2} \\ {0.875} & {2 \leq x<3} \\ {1} & {x \geq 3}\end{array}\right.$$
Work Step by Step
Determine the probability mass function of the random variable with binomial
distributions with the parameters $n=3, p=0.5 :$
$$f(x)=\left(\begin{array}{c}{3} \\ {x}\end{array}\right) 0.5^{3}, \quad x=0,1,2,3$$
Calculate the cdf:
$$F(x)=\left\{\begin{array}{ll}{0} & {x<0} \\ {f(0)=0.125} & {0 \leq x<1} \\ {0.125+f(1)=0.5} & {1 \leq x<2} \\ {0.5+f(2)=0.875} & {2 \leq x<3} \\ {1} & {x \geq 3}\end{array}\right.$$
$$F(x)=\left\{\begin{array}{ll}{0} & {x<0} \\ {0.125} & {0 \leq x<1} \\ {0.5} & {1 \leq x<2} \\ {0.875} & {2 \leq x<3} \\ {1} & {x \geq 3}\end{array}\right.$$
