Question

Following is the p. d. f. of a continuous r.v. X.

f(x) = `{(x/8,  "for"  0 < x < 4),(0,  "otherwise".):}`
Find F(x) at x = 0.5, 1.7 and 5.

Answer 1

To find
a. F(x) at x = 0.5

∴ F(0.5) = `(0.5)^2/(16) = (0.25)/(16) = (1)/(64)`

b. F(x) at x = 1.7

∴ F(1.7) = `(1.7)^2/(16) = (2.89)/(16)`

c. F(x) at x = 5

∴ F(5) = 1                  ...`[("f"(x) = 0  "if"  x ∉ (0.4)),(therefore "F"(x) = 1  "for"  x ≥ 4)]`