Unknown probabilities in a points distribution, a probability over an interval and the expected score
Unknown probabilities in a points distribution, a probability over an interval and the expected score
6 marks
At a school fair, a player throws a beanbag at a target and scores \(Y\) points. The probability distribution of \(Y\) is given in the table below, where \(k\) is a constant.
| \(y\) | \(0\) | \(2\) | \(3\) | \(5\) |
|---|---|---|---|---|
| \(\mathrm{P}(Y=y)\) | \(0.3\) | \(k\) | \(2k\) | \(0.1\) |
- Find the value of \(k\).[2]
- Find \(\mathrm{P}(1<Y\leq4)\).[2]
- Find the expected score, \(\mathrm{E}(Y)\).[2]
Solution:
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Answer:(a) \(k=0.2\) (b) \(0.6\) (c) \(\mathrm{E}(Y)=2.1\)
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