Question

1. what are the steps in computing the mean, variance and standard deviation of the probability distribution?

Explanation:

Step1: Compute the mean

The mean ($\mu$) of a probability distribution is calculated using the formula $\mu=\sum_{x}x\cdot P(x)$, where $x$ represents the values of the random variable and $P(x)$ is the corresponding probability.

Step2: Compute the variance

The variance ($\sigma^{2}$) is calculated using the formula $\sigma^{2}=\sum_{x}(x - \mu)^{2}\cdot P(x)$. First, find the deviation of each value $x$ from the mean $\mu$ ($x-\mu$), square it ($(x - \mu)^{2}$), and then multiply by the probability $P(x)$ and sum over all values of $x$.

Step3: Compute the standard deviation

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

Answer:

To compute the mean, use $\mu=\sum_{x}x\cdot P(x)$; for the variance, use $\sigma^{2}=\sum_{x}(x - \mu)^{2}\cdot P(x)$; and for the standard deviation, use $\sigma=\sqrt{\sigma^{2}}$.