Question

question 10
\begin{tabular}{|c|c|}hline x & p(x) \hline 0 & 0.25 \hline 1 & 0.05 \hline 2 & 0.25 \hline 3 & 0.45 \hlineend{tabular}
find the standard deviation of this probability distribution. give your answer to at least 2 decimal places
submit question

Explanation:

Step1: Calculate the mean ($\mu$)

$\mu=\sum_{i}x_iP(x_i)=0\times0.25 + 1\times0.05+2\times0.25 + 3\times0.45=0 + 0.05+0.5+1.35 = 1.9$

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

$\sigma^{2}=\sum_{i}(x_i-\mu)^2P(x_i)=(0 - 1.9)^2\times0.25+(1 - 1.9)^2\times0.05+(2 - 1.9)^2\times0.25+(3 - 1.9)^2\times0.45$
$=( - 1.9)^2\times0.25+( - 0.9)^2\times0.05+(0.1)^2\times0.25+(1.1)^2\times0.45$
$=3.61\times0.25 + 0.81\times0.05+0.01\times0.25+1.21\times0.45$
$=0.9025+0.0405 + 0.0025+0.5445=1.49$

Step3: Calculate the standard deviation ($\sigma$)

$\sigma=\sqrt{\sigma^{2}}=\sqrt{1.49}\approx1.22$

Answer:

$1.22$