Question

8. The continuous random variable X has pdf f(x) = { kx 0 <= x <= 2 0 otherwise [8a] (5 points) Determine the value of k that allow f(x) to be a pdf. [8b] (5 points) Determine P[-1/2 <= X <= 1/2].

          8. The continuous random variable X has pdf
f(x) = {
kx 0 <= x <= 2
0 otherwise
[8a] (5 points) Determine the value of k that allow f(x) to be a pdf.
[8b] (5 points) Determine P[-1/2 <= X <= 1/2].

Added by Matthew C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

09/17/2023

Step 1

For \( f(x) \) to be a valid pdf, the integral of \( f(x) \) over its entire domain must equal 1. The domain of \( f(x) \) is \( 0 \leq x \leq 2 \), and \( f(x) = kx \) within this interval. Therefore, we need to solve the following integral: \[ \int_{0}^{2} kx Show more…

Show all steps

Thanks for your feedback!

The continuous random variable X has a probability density function (pdf) given by: f(x) = k(x) 0 < x < 2 0 otherwise where k is a constant. Determine the value of k that allows f(x) to be a valid pdf. Determine P(-1/2 < x < 1/2).