Question

8. Following is the p. d. f. of a continuous
r. v. X.
х
for 0 < x < 4,
f(x) = {x/ 8
0 otherwise
(i) Find expression for the c. d. f. of X.
(ii) Find F(x) at x = 0.5, 1.7, and 5.​

Answer 1

Answer:

Let X be a continuous random variable with pdf f and cdf F.

By definition, the cdf is found by integrating the pdf: F(x)=x∫−∞f(t)dt.

By the Fundamental Theorem of Calculus, the pdf can be found by differentiating the cdf: f(x)=ddx[F(x)]