To find the mean and standard deviation of the given probability distribution, we can use the following formulas:

1. Mean ($\mu$):
   $\mu = \sum (x \cdot P(x))$ where $x$ is each value and $P(x)$ is the corresponding probability.

2. Variance ($\sigma^2$):
   $\sigma^2 = \sum (x^2 \cdot P(x)) - \mu^2$ where $\mu$ is the mean.

3. Standard Deviation ($\sigma$):
   $\sigma = \sqrt{\sigma^2}$

Given: