The p.d.f. of a discrete random variable is defined as f(x)= cases k x^2, & 0 x 6 0, & otherwise cases Then the value of F(4) (c.d.f) is

Step-by-step solution

aligned f (x) & = k x^2, 0 x 6 k (0)^2 & + k (1)^2+ k (2)^2+ k (3)^2+ k (4)^2 k & +4 k (5)^2+ k (6)^2=1 & 91 k =1 k & = 1 91 ~F (4) & = P ( X 4)= P ( X =0)+ P ( X =1) & = k (0)^2+ k ( k )^2+ k (2)^2+ k (3)^2+ k (4)^2 & = k +4 k +9 k +16 k & =30 k & =30 ( 1 91 ) & = 30 91 aligned