The following is p.d.f. of continuous random variable X f (x)= cases x 8 & , if 0 < x < 4 0 & , otherwise cases Then F(0 5), F(1 7) and F(5) is respectively

Step-by-step solution

The cumulative distribution function for f(x) is defined by F(x) = _ - ^x f(t)dt . For x 0 , the probability density is zero, so F(x) = 0 . Between 0 At x 4 , the integral becomes F(x) = ₀^4 t 8 dt = 16 16 = 1 . Thus, F(x) = cases 0 & x 0 x^2 16 & 0 Evaluating: F(0.5) = (0.5)^2 16 = 0.015625 0.02 , F(1.7) = 1.7^2 16 0.18 , and F(5) = 1 . These correspond to option B .