Howtosignalprocessing
- How is the maximum of a set of IID random variables distributed?
- Are max and min independent random variables?
- What is the maximum range of random variable most of the simulator can support?
- How do you find the maximum probability density?
How is the maximum of a set of IID random variables distributed?
The maximum of a set of IID random variables when appropriately normalized will generally converge to one of the three extreme value types. This is Gnedenko's theorem,the equivalence of the central limit theorem for extremes. The particular type depends on the tail behavior of the population distribution.
Are max and min independent random variables?
The min and max are a function of independent random variables, yet they have covariance. The min and the max cannot be independent.
What is the maximum range of random variable most of the simulator can support?
Variables declared with the randc keyword are random-cyclic variables that cycle through all the values in a random permutation of their declared range. Random-cyclic variables can only be reg or enumerated types, and are limited to a maximum size of 16 bits, so the maximum range for any randc variable is 0 to 65535.
How do you find the maximum probability density?
The function fX(x) gives us the probability density at point x. It is the limit of the probability of the interval (x,x+Δ] divided by the length of the interval as the length of the interval goes to 0. Remember that P(x<X≤x+Δ)=FX(x+Δ)−FX(x). =dFX(x)dx=F′X(x),if FX(x) is differentiable at x.
