If customer 1 will buy a product with a probability of 0.6 and every following customer 0.7, how can I simulate a system with n customers?
The result should show which customers bought and which didn't.
Maybe use a uniform distribution between 0 and 1 and see if the value is below the probability?
Let $i=1,...,n$ and $X_i =1$ is customer $i$ buys and $X_i=0$ if not. Let $X_i \sim Bernoulli(p_i)$ with $p_1=0.7$ and $p_i=0.6$ for $i>1$.
You can simulate it by constructing the vector $p = (p_1,...,p_n)$ then draw $U=(U_1,...,U_n)$ uniform [0,1] variables and for each $i$ let
$$X_i = I[U_i<p_i]$$
which will have the property of being 1 with probability $p_i$ following from $Pr(U_i \leq r) = \int_0^r dt = r$.
You can do this in R for example
N <- 100
p <- c(0.7,rep(0.6,N-1))
x <- as.numeric(runif(N)<p)
Generate $n$ independent uniformly distributed random variables between 0 and 1. If each variable is below the corresponding threshold, record this as a purchase. If it is above the threshold, no purchase.
