Question

find the standard deviation of this probability distribution. give your answer to at least 2 decimal places

Explanation:

Step1: Find the expected value ($\mu$)

The formula for the expected value of a discrete - random variable is $\mu=\sum_{i}x_ip_i$.
$\mu=(3\times0.5)+(2\times0.15)+(1\times0.2)+(0\times0.15)$
$=1.5 + 0.3+0.2+0$
$=2$

Step2: Calculate $(x_i - \mu)^2p_i$ for each $x_i$

For $x = 3$: $(3 - 2)^2\times0.5=1\times0.5 = 0.5$
For $x = 2$: $(2 - 2)^2\times0.15=0\times0.15 = 0$
For $x = 1$: $(1 - 2)^2\times0.2=1\times0.2 = 0.2$
For $x = 0$: $(0 - 2)^2\times0.15=4\times0.15 = 0.6$

Step3: Find the variance ($\sigma^{2}$)

The formula for the variance of a discrete - random variable is $\sigma^{2}=\sum_{i}(x_i-\mu)^2p_i$.
$\sigma^{2}=0.5 + 0+0.2+0.6$
$=1.3$

Step4: Find the standard deviation ($\sigma$)

The standard deviation is the square - root of the variance, $\sigma=\sqrt{\sigma^{2}}$.
$\sigma=\sqrt{1.3}\approx1.14$

Answer:

$1.14$