Cumulative distribution function of a DRV
Cumulative distribution function of a DRV
IB Year 6 | Grade 12
The probability distribution of a discrete random variable \(X\) is given by \(\mathrm{P}(X = x) = k\left(\frac{2}{3}\right)^x\)
where \(x = 0, 1, 2, 3, \dots\)
- Show that \(\mathrm{P}(X \leq x) = 3k\left[1 - \left(\frac{2}{3}\right)^{x+1}\right]\), where \(x = 0, 1, 2, 3, \dots\)
- Hence or otherwise, find the value of \(k\).
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 a free account to practise similar questions.
Answer:(a) \(\mathrm P(X\le x)=3k\left[1-\left(\dfrac23\right)^{x+1}\right]\), \(x=0,1,2,\ldots\) (shown). (b) \(k=\dfrac13\).
Need help? Join our JC Math tuition classes.
Learn more