I'm working on a simulation of an environment. I'm basing it on a paper that describes a mathematical model for the variables, one of them is described as:
"Analyses of these data indicated that the annual precipitation series can be well described as a normally distributed random variable ($x^2$ = 1.0, 5 df), with a mean and variance of 41.81 cm and 11.20 cm, respectively"
So I'm trying to model it with python using numpy which includes a method numpy.random.normal which randomly samples from a gaussian distribution and takes as parameters the center and standard deviation of the distribution. I understand that this parameters are the mean and the square root of the variance provided in the description but I can't figure out the meaning of the "($x^2$ = 1.0, 5 df)" part.
Could you help me understand those two concepts and how could I fit those into my simulation?
Edit: there's another variable described as:
The random variable $k_n$ represents the fact that the specific result of a particular decision is known only probabilistically. A symmetric density was assumed for $k_n$ using $D_n(X_n)$ as the mean, with probability 0.6. Values 10% above and below the mean were allowed, each with probability 0.2.
I understood that the variable can only take the value $D_n(X_n)$ with probability 0.6 OR the same value +-10% but not the values between them. Am I correct?