Find the mean and variance for the first n natural numbers

Asked by Abhisek | 1 year ago |  76

##### Solution :-

We know that Mean =

$$\dfrac{Sum\; of\; all \;observations}{Number\; of \;observations}$$

Mean, x̅ = $$\dfrac{ ((n(n + 1))2)}{n}$$

$$\dfrac{ (n + 1)}{2}$$

and also Variance,

By substitute that value of x̅ we get,

We know that,

$$(a-b)^2=a^2-2ab+b^2$$

(a + b)(a – b) = a2 – b2

σ2 = $$\dfrac{(n^2 – 1)}{12}$$

Mean = $$\dfrac{ (n + 1)}{2}$$ and Variance

$$\dfrac{(n^2 – 1)}{12}$$

Answered by Pragya Singh | 1 year ago

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