JEE PYQ: Statistics Question 22
Question 22 - 2020 (09 Jan Shift 1)
Let the observations $x_i$ $(1 \leq i \leq 10)$ satisfy the equations, $\sum_{i=1}^{10}(x_i - 5) = 10$ and $\sum_{i=1}^{10}(x_i - 5)^2 = 40$. If $\mu$ and $\lambda$ are the mean and the variance of the observations $x_1 - 3, x_2 - 3, \ldots, x_{10} - 3$, then the ordered pair $(\mu, \lambda)$ is equal to:
(1) $(3, 3)$ (2) $(6, 3)$ (3) $(6, 6)$ (4) $(3, 6)$
Show Answer
Answer: (1) $(3, 3)$
Solution
$\mu = \bar{x} - 3 = 6 - 3 = 3$. $\lambda = \text{Var}(x_i) = 3$. $(\mu, \lambda) = (3, 3)$.
BETA
