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13.Statistics
medium
આવુતિ વિતરણ
| $X$ | $c$ | $2c$ | $3c$ | $4c$ | $5c$ | $6c$ |
| $f$ | $2$ | $1$ | $1$ | $1$ | $1$ | $1$ |
નુંવિચરણ જો $160$ હોય તો $\mathrm{c} \in \mathrm{N}$ નું મૂલ્ય ............ છે.
A
$5$
B
$8$
C
$7$
D
$6$
(JEE MAIN-2024)
Solution
| $x$ | $C$ | $2C$ | $3C$ | $4C$ | $5C$ | $6C$ |
| $f$ | $2$ | $1$ | $1$ | $1$ | $1$ | $1$ |
$\bar{x}=\frac{(2+2+3+4+5+6) C}{7}=\frac{22 C}{7}$
$ \operatorname{Var}(\mathrm{x})=\frac{\mathrm{c}^2\left(2+2^2+3^2+4^2+5^2+6^2\right)}{7} $
$ -\left(\frac{22 c}{7}\right)^2 $
$ =\frac{92 c^2}{7}-\mathrm{c}^2 \times \frac{484}{49} $
$ =\frac{(644-484) c^2}{49}=\frac{160 c^2}{49} $
$ 160=\frac{160 \times c^2}{49} \Rightarrow c=7$
Standard 11
Mathematics
