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Unknown value of a discrete random variable from a quadratic probability formula and its expected value

Unknown value of a discrete random variable from a quadratic probability formula and its expected value

7 marks

A discrete random variable \(X\) takes the values \(1\), \(2\) and \(k\), where \(k>0\), with \(\mathrm{P}(X=x)=\dfrac{x(x+1)}{50}\).

  1. Write down \(\mathrm{P}(X=1)\).[1]
  2. Show that \(k=6\).[4]
  3. Find \(\mathrm{E}(X)\).[2]

Solution:

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Answer:(a) \(\dfrac{1}{25}\) (b) \(k=6\) (shown) (c) \(\mathrm{E}(X)=\dfrac{133}{25}=5.32\)

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