Question

consider the discrete random variable x given in the table below. calculate the mean, variance, and standard deviation of x. round answers to two decimal places.
what is the expected value of x?

Explanation:

Step1: Calculate the mean ($\mu$ or expected value $E(X)$)

The formula for the mean of a discrete - random variable is $E(X)=\sum_{i}x_ip_i$.

$$
LATEXBLOCK0
$$

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

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

$$
LATEXBLOCK1
$$

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

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

$$ \sigma=\sqrt{16.52190}\approx4.06 $$

Answer:

$\mu = 5.69$
$\sigma^{2}=16.52$
$\sigma = 4.06$
Expected value of $X$: $5.69$