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Mean and variance of a random variable — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMean and variance of a random variable2 Marks
Question
The probability distribution function oif a random variable X is given by
$X_i$ 0 1 2
$P_i$ $3c^3$ $4c - 10c^2$ 5c - 1
Where c > 0
Find: c.
✓

Answer

We know that the sum of the probabilities in a probability distribution is always 1.
$\therefore P(X = 0) + P(X = 1) + P(X = 2) = 1$
$\Rightarrow 3c^3 + 4c - 10c^2+ 5c - 1 = 1$
$\Rightarrow 3c^3 - 10c^2 + 9c - 2 = 0$
$\Rightarrow (c - 1)(3c^2 - 7c + 2) = 0$
$\Rightarrow (c - 1)(3c - 1)(c - 2) = 0$
$\Rightarrow\text{c}=\frac{1}{3},1,2$
(Negleting 1 and 2 as individual probability should not be greater than one)

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