Question

consider the discrete random variable x given in the table below. calculate the mean, variance, and standard deviation of x. round to 4 decimals.

x	2	4	7	18
p(x)	0.11	0.07	0.12	0.7

μ =
σ² =
σ =

what is the expected value of x?

Explanation:

Step1: Calculate the mean (expected value)

The formula for the mean $\mu = E(X)=\sum_{i}x_{i}P(x_{i})$.

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Step2: Calculate the variance

The formula for the variance $\sigma^{2}=\sum_{i}(x_{i}-\mu)^{2}P(x_{i})$.

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Step3: Calculate the standard deviation

The standard deviation $\sigma=\sqrt{\sigma^{2}}$.
$\sigma=\sqrt{39.9164}\approx6.3179$

Answer:

$\mu = 13.9400$
$\sigma^{2}=39.9164$
$\sigma = 6.3179$
The expected value of $X$ is $13.9400$