Question

A coin with P[H]=0.3 is flipped 3 times. Define N to be the total number of heads. Find the CDF FN(n), the cumulative distribution function for N. (please provide an explanation for the answer)

Answer 1

here F(n)= 0   if -$\infty$ < n<1

F(n)=³C₀(0.3)⁰(0.7)³ =0.343 if 0 <=n <1

F(n)=0.343+³C₁(0.3)¹(0.7)² =0.343+0.441 =0.784     if 1 <=n<2

F(n)=0.784+³C₁(0.3)¹(0.7)² =0.973   if 2<=n <3

F(n)=1 if 3<=n <$\infty$