Practicing Success
The probability distribution of X is :
Then var(X) = |
$\frac{3}{20}$ $\frac{9}{4}$ $\frac{141}{20}$ $\frac{159}{80}$ |
$\frac{159}{80}$ |
⇒ 0.1 + 2k + k + k + 2k = 1 ⇒ 6k = 0.7 so $k = \frac{0.9}{6} = \frac{9}{60} = \frac{3}{20}$ so var(X) = E(X2) - E2(X) = 02 × 0.1 + 12 × 2k + 22 × k + 32 × k + 42 × 2k - (0 × 0.1 + 1 × 2k + 2 × k + 3 × k + 4 × 2k)2 = 2k + 4k + 9k + 32k - (2k + 2k + 3k + 8k)2 = 47 - (15k)2 = 47k - 225k2 = $47 × \frac{3}{20} - 225 × \frac{9}{400}$ = $\frac{141}{20} - \frac{81}{16}$ = $\frac{564 - 405}{80}$ = $\frac{159}{80}$ |