Finding unknown constant in pdf
Finding unknown constant in pdf
IB Year 5 | Grade 11
The probability density function (p.d.f.) of a discrete random variable \(Y\) is given by
\[P(Y = y) = ky^2, \quad y = 1, 2, 3, 4, 5,\]
where \(k\) is a constant.
- Find the value of \(k\).
- Hence find (a) \(P(Y < 2)\), (b) \(P(1 < Y \le 3)\) and (c) \(P(Y > 3)\).
Solution:
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Answer:(i) \(k=\frac1{55}\). (ii)(a) \(\frac1{55}\) (b) \(\frac{13}{55}\) (c) \(\frac{41}{55}\).
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