Statistics
Variance of Discrete Distribution
MMTS_Full_Test_20
Grade 12
Question:
Two dice $A$ and $B$ are rolled. Let the numbers obtained on $A$ and $B$ be $\alpha,\beta$ respectively. If the variance of random variable $\alpha-\beta$ is $\dfrac{k_1}{k_2}$, where $k_1$ and $k_2$ are co-prime, then $k_1-k_2=$
Step-by-Step Solution
Key Concept: $\text{Var}(\alpha-\beta)=\text{Var}(\alpha)+\text{Var}(\beta)$; variance of single die = 35/12
Var(single die)$=\frac{35}{12}$. Var$(\alpha-\beta)=\frac{35}{12}+\frac{35}{12}=\frac{35}{6}$. $k_1=35, k_2=6$. $k_1-k_2=29$.
Correct Answer: 2