Tim Gan Math
Sign up free

Finding the value of an unknown in a CRV

Finding the value of an unknown in a CRV

IB Year 5 | Grade 11

The continuous random variable \(X\) has probability density function given by

\[\mathrm{f}(x) = \begin{cases} k & , \quad 0 \leq x < 2 \\ k(2x - 3) & , \quad 2 \leq x \leq 3 \\ 0 & , \quad \text{otherwise} \end{cases}\]

  1. Find the value of the constant \(k\).
  2. Sketch the graph of \(y = \mathrm{f}(x)\).
  3. Find \(\mathrm{P}(X \leq 1)\).
  4. Find \(\mathrm{P}(X > 2.5)\).
  5. Find \(\mathrm{P}(1 \leq X \leq 2.3)\).

Solution:

Solution locked

680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs tuition enrolment.

Create free accountSign inIB Math tuition

Create a free account to practise similar questions.

Create free accountSign inIB Math tuition
Answer:(a) \(k=1/4\); (b) see sketch; (c) \(1/4\); (d) \(5/16\); (e) \(139/400\).

Need help? Join our JC Math tuition classes.

Learn more