...
If a != 1, then
If a != 1, then
where, k factorial = k! = (k)(k - 1)(k - 2)(...)(1).
Combinations of Choosing k from n Elements
Frequently Used Random Variables
Exponential Continuous Random Variable
RV X with parameter α parameter α > 0.Supports that supports [0, ∞)
Memoryless property:
Uniform Continuous Random Variable
RV X.Supports that supports [a, b]
Bernoulli Discrete Random Variable
RV X with parameter 0 < p < 1.Supports k that supports k = {0, 1}
Binomial Discrete Random Variable
RV X with parameters positive integer n > 0, and 0 < p < 1.Supports k that supports k = {0, 1, ..., n}
Geometric Discrete Random Variable
RV X with parameter 0 < p < 1 indicating the probability of success.
The number X of Bernoilli trials needed to get one success, supported on the set k = {1, 2, ...}.
Memoryless property:
The number of Y = X - 1 failures before the first success, supported on the set k = {0, 1, ...}.
Poisson Discrete Random Variable
RV X with parameter λ > 0.Supports k that supports k = {0, 1, ...}
