Question

check here for instructional material to complete this problem. find $mu$ if $mu=sum xcdot p(x)$. then, find $sigma$ if $sigma^{2}=sum x^{2}cdot p(x)-mu^{2}$.

x	0	1	2	3	4	5
p(x)	0.5584	0.3451	0.0853	0.0105	0.0007	0.0000

$mu=square$ (simplify your answer. round to four decimal places as needed.)
$sigma=square$ (simplify your answer. round to four decimal places as needed.)

Explanation:

Step1: Calculate the mean $\mu$

$$\mu=\sum[x\cdot P(x)]=0\times0.5584 + 1\times0.3451+2\times0.0853 + 3\times0.0105+4\times0.0007+5\times0.0000$$
$$=0 + 0.3451+0.1706+0.0315 + 0.0028+0$$
$$=0.549999\approx0.5500$$

Step2: Calculate $\sum[x^{2}\cdot P(x)]$

$$\sum[x^{2}\cdot P(x)]=0^{2}\times0.5584 + 1^{2}\times0.3451+2^{2}\times0.0853 + 3^{2}\times0.0105+4^{2}\times0.0007+5^{2}\times0.0000$$
$$=0\times0.5584+1\times0.3451 + 4\times0.0853+9\times0.0105 + 16\times0.0007+25\times0.0000$$
$$=0 + 0.3451+0.3412+0.0945+0.0112+0$$
$$=0.792$$

Step3: Calculate the variance $\sigma^{2}$

$$\sigma^{2}=\sum[x^{2}\cdot P(x)]-\mu^{2}=0.792-(0.5500)^{2}$$
$$=0.792 - 0.3025=0.4895$$

Step4: Calculate the standard - deviation $\sigma$

$$\sigma=\sqrt{\sigma^{2}}=\sqrt{0.4895}\approx0.6996$$

Answer:

$\mu = 0.5500$
$\sigma = 0.6996$