Statistics
Mean and Variance from Distribution Table with Unknown k
nta_pyq_2023_apr
Grade 11
Question:
For the distribution $X_i: 0,1,2,3,4,5$; $f_i: k+2,2k,k^2-1,k^2-1,k^2+1,k-3$ with $\sum f_i=62$, then $[\mu^2+\sigma^2]$ is equal to
Step-by-Step Solution
Key Concept: $\sum f_i=3k^2+4k-2=62\Rightarrow k=4$. Compute $\mu$ and $\sigma^2$.
$k=4$, $\mu^2+\sigma^2=\frac{500}{62}$. $[\cdot]=8$.
Correct Answer: 2