The random variables X1, X2, ..., Xi, ... are independent and identically distributed random variables each with density f(x) and characteristic function x(u)=E[eʲᵘˣ]. Consider a Poisson process with rate lambda. The number of events that occur in the interval (0, t] is denoted by N(t). Which of the following is true about N(t)?
1) N(t) is a continuous random variable
2) N(t) is a discrete random variable
3) N(t) follows a normal distribution
4) N(t) follows a Poisson distribution