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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: P (X < 2)
Solution
P (X < 2)
\[= P\left( X = 0 \right) + P\left( X = 1 \right)\]
\[ = 3 c^3 + 4c - 10 c^2 \]
\[ = \frac{1}{9} + \frac{4}{3} - \frac{10}{9}\]
\[ = \frac{1 + 12 - 10}{9}\]
\[ = \frac{3}{9}\]
\[ = \frac{1}{3}\]
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