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Home » For the following probability distribution determine standard deviation of the random variable X.
For the following probability distribution determine standard deviation of the random variable X.
CBSE | Class 12 | Exercise 1 | Maths | NCERT Exemplar | Probability
For the following probability distribution determine standard deviation of the random variable X.

We know that: Standard deviation (S.D.) =

    \[\sqrt{Variance}\]

So,

    \[Var\left( X \right)\text{ }=\text{ }E({{X}^{2}})\text{ }\text{ }{{\left[ E\left( X \right) \right]}^{2}}\]

    \[E\left( X \right)\text{ }=\text{ }2\text{ }\times \text{ }0.2\text{ }+\text{ }3\text{ }\times 0.5\text{ }+\text{ }4\text{ }\times 0.3\text{ }=\text{ }0.4\text{ }+\text{ }1.5\text{ }+\text{ }1.2\text{ }=\text{ }3.1\]

    \[E({{X}^{2}})\text{ }=\text{ }4\text{ }\times \text{ }0.2\text{ }+\text{ }9\text{ }\times \text{ }0.5\text{ }+\text{ }16\text{ }\times \text{ }0.3\text{ }=\text{ }0.8\text{ }+\text{ }4.5\text{ }+\text{ }4.8\text{ }=\text{ }10.1\]

⇒

    \[V\left( X \right)\text{ }=\text{ }10.1\text{ }\text{ }{{\left( 3.1 \right)}^{2}}~=\text{ }10.1\text{ }\text{ }9.61\text{ }=\text{ }0.49\]

Therefore, S.D. =

    \[\sqrt{0.49}\text{ }=\text{ }0.7\]

i

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