If a discrete random variable X has the following probability distribution:
X: $\frac{1}{2} 1 \frac{3}{2} 2$
P(X): c c² 2c² c
Then, c = ____________.

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Solution

For a discrete random variable,
Since sum of probability is 1
∴ c + c² + 2c² + c = 1
i.e. 3c² + 2c = 1
i.e. 3c² + 2c − 1 = 0
i.e. 3c² + 3c − c − 1 = 0
i.e. 3c (c + 1) − 1 (c + 1) = 0
i.e. c = $\frac{1}{3}$ (∵ c ≠ −1)

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