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Question
The probability distribution function of a random variable X is given by
| xi : | 0 | 1 | 2 |
| pi : | 3c3 | 4c − 10c2 | 5c-1 |
where c > 0 Find: c
Solution
We know that the sum of probabilities in a probability distribution is always 1.
∴ P (X = 0) + P (X = 1) + P (X = 2) = 1
\[\Rightarrow 3 c^3 + 4c - 10 c^2 + 5c - 1 = 1\]
\[ \Rightarrow 3 c^3 - 10 c^2 + 9c - 2 = 0\]
\[ \Rightarrow \left( c - 1 \right)\left( 3 c^2 - 7c + 2 \right) = 0\]
\[ \Rightarrow \left( c - 1 \right)\left( 3c - 1 \right)\left( c - 2 \right) = 0\]
\[ \Rightarrow c = \frac{1}{3}, 1, 2\]
\[\left( \text{ Neglecting 1 and 2 as individual probability should not be greater than one} \right)\]
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