Question

A continuous random variable X has the following distribution function
F(x) = `{{:(0",",  "if"  x ≤ 1),("k"(x - 1)^4",",  "if"  1 < x ≤ 3),(1",",  "if"  x > 3):}`
Find k

Answer 1

Here F(3) – F(1) = 1

k(3 – 1)⁴ – 0 = 1

k(2)⁴ = 1

k(16) = 1

k = `1/16`