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Statement $1$ : The variance of first $n$ odd natural numbers is $\frac{{{n^2} - 1}}{3}$
Statement $2$ : The sum of first $n$ odd natural number is $n^2$ and the sum of square of first $n$ odd natural numbers is $\frac{{n\left( {4{n^2} + 1} \right)}}{3}$
Statement $1$ is true, Statement $2$ is false.
Statement $1$ is true, Statement $2$ is true;
Statement $2$ is not a correct explanation for Statement $1$.
Statement $1$ is false, Statement $2$ is true.
Statement $1$ is true, Statement $2$ is true,
Statement $2$ is a correct explanation for Statement $1$.
Solution
Statement $2$ : Sum of first $n$ odd natural numbers is not equal to $n^2$ So, statement $- 2$ is false.
Similar Questions
Let $\mathrm{X}$ be a random variable with distribution.
$\mathrm{x}$ | $-2$ | $-1$ | $3$ | $4$ | $6$ |
$\mathrm{P}(\mathrm{X}=\mathrm{x})$ | $\frac{1}{5}$ | $\mathrm{a}$ | $\frac{1}{3}$ | $\frac{1}{5}$ | $\mathrm{~b}$ |
If the mean of $X$ is $2.3$ and variance of $X$ is $\sigma^{2}$, then $100 \sigma^{2}$ is equal to :