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A biased die is such that \[\mathbf{P}\left( \mathbf{4} \right)\text{ }=\text{ }\mathbf{1}/\mathbf{10}\]and other scores being equally likely. The die is tossed twice. If X is the ‘number of fours seen’, find the variance of the random variable X.
A biased die is such that \[\mathbf{P}\left( \mathbf{4} \right)\text{ }=\text{ }\mathbf{1}/\mathbf{10}\]and other scores being equally likely. The die is tossed twice. If X is the ‘number of fours seen’, find the variance of the random variable X.
CBSE | Class 12 | Exercise 1 | Maths | NCERT Exemplar | Probability
A biased die is such that \[\mathbf{P}\left( \mathbf{4} \right)\text{ }=\text{ }\mathbf{1}/\mathbf{10}\]and other scores being equally likely. The die is tossed twice. If X is the ‘number of fours seen’, find the variance of the random variable X.

Here, random variable \[X\text{ }=\text{ }0,\text{ }1,\text{ }2\]

\[P\left( X\text{ }=\text{ }2 \right)\text{ }=\text{ }P\left( 4 \right).P\left( 4 \right)\text{ }=\text{ }1/10\text{ }x\text{ }1/10\text{ }=\text{ }1/100\]

Now, we know \[V\left( X \right)\text{ }=\text{ }E({{X}^{2}})\text{ }\text{ }{{\left[ E\left( X \right) \right]}^{2}}\]

Therefore, the required variance = \[0.18\].

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