#########################################################################
## This function returns the value of the probability density function ##
## of a mixed Poisson distributed random variable with the parameters  ##
## given in exercise 1, sheet #5                                       ##
#########################################################################

pdf_N <- function(k) {
	lambda <- c(60,35,16,12,6)
	p <- c(0.05,0.2,0.4,0.25,0.1)
	sum <- NULL
	for (i in 1:length(k)) {
		temp <- exp(-lambda)*lambda^k[i]/factorial(k[i])
		sum <- c(sum,t(p)%*%temp)
	}
	return(sum)
}

## Example 1: value of the pdf at k=1
pdf_N(1)

## Example 2: value of the pdf at k=1,3,5
k <- c(1,3,5)
pdf_N(k)