Probability distribution whose probabilities are proportional to the terms of an arithmetic sequence
Probability distribution whose probabilities are proportional to the terms of an arithmetic sequence
6 marks
The terms of an arithmetic sequence satisfy \(u_2=0.7\) and \(u_5=0.1\).
- Find \(d\), the common difference of the sequence.[2]
A discrete random variable \(Y\) takes the values \(1\), \(2\), \(3\), \(4\) and \(5\), with \(\mathrm{P}(Y=n)=\frac{u_n}{k}\) for each value \(n\), where \(k\) is a positive constant. Its probability distribution is given in the table.
| \(n\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) |
|---|---|---|---|---|---|
| \(\mathrm{P}(Y=n)\) | \(\frac{u_1}{k}\) | \(\frac{0.7}{k}\) | \(\frac{u_3}{k}\) | \(\frac{u_4}{k}\) | \(\frac{0.1}{k}\) |
- Find \(k\).[4]
Solution:
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Answer:(a) \(d=-0.2\) (b) \(k=2.5\)
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