To calculate the mean $\mu_X$ and standard deviation $\sigma_X$ of a discrete random variable, we use the following formulas:

1. Mean ($\mu_X$):

$\mu_X = \sum [x \cdot P(x)]$ This means we take each value $x$, multiply it by its corresponding probability $P(x)$, and then sum these products.

2. Standard Deviation ($\sigma_X$):

$\sigma_X = \sqrt{ \sum [x^2 \cdot P(x)] - \mu_X^2 }$ This requires first calculating $\sum [x^2 \cdot P(x)]$ and then subtracting the square of the mean, $\mu_X^2$, from it. Finally, take the square root to find $\sigma_X$.

Steps to compute:

1. List the values of $x$ and their corresponding probabilities $P(x)$.
2. Compute $\sum [x \cdot P(x)]$ to find the mean $\mu_X$.
3. Compute $\sum [x^2 \cdot P(x)]$.
4. Plug these into the formula for $\sigma_X$ and compute the standard deviation.

Please provide the values of $x$ and $P(x)$ so I can help you compute the mean and standard deviation.