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Finding the value of an unknown in CRV

Finding the value of an unknown in CRV

IB Year 5 | Grade 11

The continuous random variable \(X\) has probability density function \(\mathrm{f}(x) = kx^2\), where \(0 \le x \le 2\).

  1. Find the value of the constant \(k\).
  2. Sketch the graph of \(y = \mathrm{f}(x)\).
  3. Find \(\mathrm{P}(X \ge 1)\).
  4. Find \(\mathrm{P}(0.5 \le X < 1.5)\).

Solution:

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Answer:(i) \(k=3/8\); (ii) see sketch; (iii) \(7/8\); (iv) \(13/32\).

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