Finding unknown constant in a probability distribution function
Finding unknown constant in a probability distribution function
IB Year 6 | Grade 12
The probability density function of the discrete random variable \(X\) is given by
\[P(X=x)=a\left(\frac{3}{4}\right)^x \text{ for}\hspace{0.5em} x=0,1,2,...\]
- Find the value of the constant \(a\).
- Find the values of \(P(X<3)\) and \(P(X>2)\).
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Answer:(i) \(a=\dfrac14\) (ii) \(P(X<3)=\dfrac{37}{64}\), \(P(X>2)=\dfrac{27}{64}\)
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