Two dice A and B are rolled. Let the numbers obtained on A and B be respectively. If the variance of random variable is k 1 k 2 , where k 1 and k 2 are co-prime, then k 1 - k 2 =

Question

Two dice A and B are rolled. Let the numbers obtained on A and B be $α, β$ respectively. If the variance of random variable $α - β$ is $\frac{k_{1}}{k_{2}}$ , where $k_{1}$ and $k_{2}$ are co-prime, then $k_{1} - k_{2} =$ _______

Smart Achievers · Accepted Answer

(2)

$α - β$	$5$	$4$	$3$	$2$	$1$	$k_{1} - k_{2} =$	$- 1$	$- 2$	$- 3$	$- 4$	$- 5$
$Prob$	$\frac{1}{36}$	$\frac{2}{36}$	$\frac{3}{36}$	$\frac{4}{36}$	$\frac{5}{36}$	$\frac{1}{6}$	$\frac{5}{36}$	$\frac{4}{36}$	$\frac{1}{12}$	$\frac{1}{18}$	$\frac{1}{36}$

Solution

Q.
Two dice A and B are rolled. Let the numbers obtained on A and B be $α, β$ respectively. If the variance of random variable $α - β$ is $\frac{k_{1}}{k_{2}}$ , where $k_{1}$ and $k_{2}$ are co-prime, then $k_{1} - k_{2} =$ _______

1 21

2 29

3 13

4 19

Ans.
(2)

$α - β$ $5$ $4$ $3$ $2$ $1$ $0$ $- 1$ $- 2$ $- 3$ $- 4$ $- 5$

$Prob$ $\frac{1}{36}$ $\frac{2}{36}$ $\frac{3}{36}$ $\frac{4}{36}$ $\frac{5}{36}$ $\frac{1}{6}$ $\frac{5}{36}$ $\frac{4}{36}$ $\frac{1}{12}$ $\frac{1}{18}$ $\frac{1}{36}$

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