Question

section 6.1 homework
due monday by 11:59pm points 21 submitting an external tool
section 6.1 homework
score: 7.67/21 answered: 8/21
question 11
consider the discrete random variable x given in the table below. calculate the standard deviation of x. round answers to two decimal places.

x	3	10	12	14	19
p(x)	0.13	0.59	0.12	0.08	0.08

μ =
σ² =
σ =
what is the expected value of x?

Explanation:

Step1: Calculate the expected value $\mu$

The formula for the expected value of a discrete - random variable is $\mu=\sum_{i}x_ip_i$.
$\mu = 3\times0.13+10\times0.59 + 12\times0.12+14\times0.08+19\times0.08$
$=0.39 + 5.9+1.44 + 1.12+1.52$
$=10.37$

Step2: Calculate the variance $\sigma^{2}$

The formula for the variance of a discrete - random variable is $\sigma^{2}=\sum_{i}(x_i-\mu)^2p_i$.
$(3 - 10.37)^2\times0.13+(10 - 10.37)^2\times0.59+(12 - 10.37)^2\times0.12+(14 - 10.37)^2\times0.08+(19 - 10.37)^2\times0.08$
$=(-7.37)^2\times0.13+(-0.37)^2\times0.59+(1.63)^2\times0.12+(3.63)^2\times0.08+(8.63)^2\times0.08$
$=54.3169\times0.13 + 0.1369\times0.59+2.6569\times0.12 + 13.1769\times0.08+74.4769\times0.08$
$=7.061197+0.080771+0.318828+1.054152+5.958152$
$=14.473099\approx14.47$

Step3: Calculate the standard deviation $\sigma$

The standard deviation is the square - root of the variance, $\sigma=\sqrt{\sigma^{2}}$.
$\sigma=\sqrt{14.47}\approx3.80$

Answer:

$\mu = 10.37$, $\sigma^{2}=14.47$, $\sigma = 3.80$