Question

Let X be a random variable with p.d.f. f(x) =6x(1-x), 0\(\le\) x \(\le\)1. Determine the value of b such that P(X < b)=P(X > b).
1. \(\frac{1}{2}\)
2. \(\frac{1 \mp \sqrt{3}}{2}\)
3. 0
4. \(\frac{1}{3}\)

• A. \(\frac{1}{2}\)
• B. \(\frac{1 \mp \sqrt{3}}{2}\)
• C. 0
• D. \(\frac{1}{3}\)

Hint:

Always look for symmetry in continuous probability density functions first.
If the function is symmetric, the median is always the midpoint of the interval, saving you from performing tedious cubic integration.

Answer 1

The Correct Option is A