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Cumulative distribution function of a DRV

Cumulative distribution function of a DRV

IB Year 6 | Grade 12

The discrete random variable \(X\) has cumulative distribution function given by \(\mathrm{P}(X \le x) = kx\)

where \(x = 1, 2, 3, \dots, n\).

  1. Find the value of \(k\) in terms of \(n\).
  2. Find the probability distribution of \(X\), \(\mathrm{P}(X = x)\), in terms of \(n\).

Solution:

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Answer:Taking \(1,\ldots,n\) as the complete support: (a) \(k=\frac1n\). (b) \(\mathrm{P}(X=j)=\frac1n\) for \(j=1,\ldots,n\), and \(0\) otherwise.

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