Question

check here for instructional material to complete this problem. find μ if μ = ∑x·p(x). then, find σ if σ² = ∑x²·p(x) - μ².

x	0	1	2	3	4	5
p(x)	0.0116	0.0834	0.2399	0.3452	0.2484	0.0715

μ = (simplify your answer. round to four decimal places as needed.)

Explanation:

Step1: Calculate the mean $\mu$

$\mu=\sum_{x}[x\cdot P(x)]=0\times0.0116 + 1\times0.0834+2\times0.2399 + 3\times0.3452+4\times0.2484+5\times0.0715$
$=0 + 0.0834+0.4798+1.0356+0.9936+0.3575$
$=2.9499$

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

$\sum_{x}[x^{2}\cdot P(x)]=0^{2}\times0.0116 + 1^{2}\times0.0834+2^{2}\times0.2399 + 3^{2}\times0.3452+4^{2}\times0.2484+5^{2}\times0.0715$
$=0\times0.0116+1\times0.0834 + 4\times0.2399+9\times0.3452+16\times0.2484+25\times0.0715$
$=0 + 0.0834+0.9596+3.1068+3.9744+1.7875$
$=10.9117$

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

$\sigma^{2}=\sum_{x}[x^{2}\cdot P(x)]-\mu^{2}=10.9117-(2.9499)^{2}$
$=10.9117 - 8.6919$
$=2.2198$

Step4: Calculate the standard - deviation $\sigma$

$\sigma=\sqrt{\sigma^{2}}=\sqrt{2.2198}\approx1.4900$

Answer:

$\mu = 2.9499$, $\sigma\approx1.4900$