Question

The CDF for a certain random variable is given as F(x) = {0, -∞<x≤0; kx2, 0<x≤10; 100k, 10<x<∞;} The value of k is __________

(a) 100

(b) 50

(c) 1/50

(d) 1/100

This question was posed to me in final exam.

I'd like to ask this question from Properties of ROC in section Laplace Transform and System Design of Signals and Systems

Answer 1

Right choice is (d) 1/100

To explain I would say: From the given F(x),

We get, \(\frac{dF(x)}{dx}\) = 0 + 2kx + 0

= 2kx

∴ \(\int_0^{10}\) 2 kx dx =1

Or, 100k = 1

Or, k = 1/100.