Probability
Random variable on a line — variance
MJAT_TS7_P1
Grade 12
Question:
Let $X$ be a random variable with $P(X=x)$ lying on a line for $x=0,1,2,3,4$ and $P(X=x)=0$ otherwise. If mean $=\dfrac{5}{2}$ and variance $=\alpha$, then $24\alpha$ equals:
Step-by-Step Solution
Key Concept: $P(X=x)=mx+n$ (linear). From $\sum P(X=x)=1$: $10m+5n=1$. From mean $\sum xP(X=x)=5/2$: $30m+10n=5/2$. Solve: $m=1/20$, $n=1/10$. So $P(X=x)=(x+2)/20$.
$24\alpha=\mathbf{42}$.
Correct Answer: 42