Let sets A and B have 5 elements each. Let th | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $A = \{a_1, a_2, a_3, a_4, a_5\}$ and $B = \{b_1, b_2, b_3, b_4, b_5\}$.Given,$\overline{A} = 5 \implies \sum a_i = 25$ and $\overline{B} = 8

Vedclass · Accepted Answer

$38$

Vedclass · Answer

(B) Let $A = \{a_1, a_2, a_3, a_4, a_5\}$ and $B = \{b_1, b_2, b_3, b_4, b_5\}$.Given,$\overline{A} = 5 \implies \sum a_i = 25$ and $\overline{B} = 8 \implies \sum b_i = 40$.Variance $\sigma_A^2 = 12 \implies \frac{\sum a_i^2}{5} - 5^2 = 12 \implies \sum a_i^2 = 5(37) = 185$.Variance $\sigma_B^2 = 20 \implies \frac{\sum b_i^2}{5} - 8^2 = 20 \implies \sum b_i^2 = 5(84) = 420$.Set $C$ consists of $a_i - 3$ and $b_i + 2$ for $i=1$ to $5$.Mean of $C$,$\overline{C} = \frac{\sum (a_i - 3) + \sum (b_i + 2)}{10} = \frac{(25 - 15) + (40 + 10)}{10} = \frac{60}{10} = 6$.Variance of $C$,$\sigma_C^2 = \frac{\sum (a_i - 3)^2 + \sum (b_i + 2)^2}{10} - (\overline{C})^2$.$\sum (a_i - 3)^2 = \sum a_i^2 - 6\sum a_i + 45 = 185 - 6(25) + 45 = 80$.$\sum (b_i + 2)^2 = \sum b_i^2 + 4\sum b_i + 20 = 420 + 4(40) + 20 = 600$.$\sigma_C^2 = \frac{80 + 600}{10} - 6^2 = 68 - 36 = 32$.Sum of mean and variance $= 6 + 32 = 38$.

$x$	$2$	$6$	$8$	$9$
$f$	$4$	$4$	$\alpha$	$\beta$

Similar Questions

The sum of two positive integers is $100$. The probability that their product is greater than $1000$ is

For $(2n+1)$ observations ${x_1}, -{x_1}, {x_2}, -{x_2}, ....., {x_n}, -{x_n}$ and $0$,where all $x_i$ are distinct,let $S.D.$ and $M.D.$ denote the standard deviation and median respectively. Which of the following is always true?

The mean and variance of seven observations are $8$ and $16$ respectively. If $5$ of the observations are $2, 4, 10, 12, 14$, then the square root of the product of the remaining two observations is (in $\sqrt{3}$)

Let the mean and variance of the frequency distribution be $6$ and $6.8$ respectively.

$x$ $2$ $6$ $8$ $9$

$f$ $4$ $4$ $\alpha$ $\beta$

If $x_{3}$ is changed from $8$ to $7$,then the mean for the new data will be:

Which one of the following is false?

Vedclass Test Series

Exam Paper Generator

Online Exam Module