Question #67bb2

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Answer 1 · 2015-09-08T04:23:56

$c = \frac{10}{3}$ $c = 10/3$

$E (x) = \sum x \cdot P (x)$ $E(x) = sum x* P(x)$

Properties of p.d.f. include $\sum p (x) = 1$ $sump(x) = 1$

$\sum P (x) = 1$ $sum P(x) = 1$

=> $c [1 + 4 + 9 + 16] = 1$ $c[1 +4 + 9 + 16 ] = 1$

=> $30 c = 1$ $30c = 1$

=> $c = \frac{1}{30} . E (x)$ $c = 1/30.E(x)$

$= (\frac{1}{30}) [1 . 1^{2} + 2 . 2^{2} + 3 . 3^{2} + 4 . 4^{2}]$ $= (1/30) [1 . 1^2 + 2. 2^2 + 3. 3^2 + 4. 4^2 ]$

$= (\frac{1}{30}) [1 + 8 + 27 + 64]$ $= (1/30)[ 1 + 8 + 27 + 64]$

$= \frac{100}{30}$ $= 100/30$

$= \frac{10}{3}$ $= 10/3$

$E (x) = \sum x \cdot P (x)$ $E(x) = sum x* P(x)$