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Unknown constant in a discrete probability distribution from a quadratic equation, then the expected value

Unknown constant in a discrete probability distribution from a quadratic equation, then the expected value

7 marks

The discrete random variable \(Y\) has the probability distribution shown, where \(k\) is a constant.

\(y\)\(-2\)\(1\)\(3\)\(5\)
\(\mathrm{P}(Y=y)\)\(0.25\)\(6k^2\)\(0.31\)\(k\)
  1. Find the value of \(k\).[4]
  2. Find \(\mathrm{E}(Y)\).[3]

Solution:

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Answer:(a) \(k=0.2\) (b) \(\mathrm{E}(Y)=1.67\)

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