##Scenario, 5 out of 30 who receive procedure die in 30 days, national proportion of death is 0.05.
5/30
## [1] 0.1666667
dbinom(5, 30, 0.05)
## [1] 0.01235302
#Comparing our scenario with someone having 0 deaths in 30 procedures
dbinom (0, 30, 0.05)
## [1] 0.2146388
#probability of one death in 30 procedures
dbinom (1, 30, 0.05)
## [1] 0.3389033
##plotting all possible outcomes
x <- c(0:30)
y <- c(dbinom(0, size = 30, prob = .05),dbinom(1, size = 30, prob = .05),dbinom(2, size = 30, prob = .05),dbinom(3, size = 30, prob = .05),dbinom(4, size = 30, prob = .05),dbinom(5, size = 30, prob = .05),dbinom(6, size = 30, prob = .05),dbinom(7, size = 30, prob = .05),dbinom(8, size = 30, prob = .05),dbinom(9, size = 30, prob = .05),dbinom(10, size = 30, prob = .05),dbinom(11, size = 30, prob = .05),dbinom(12, size = 30, prob = .05),dbinom(13, size = 30, prob = .05),dbinom(14, size = 30, prob = .05),dbinom(15, size = 30, prob = .05),dbinom(16, size = 30, prob = .05),dbinom(17, size = 30, prob = .05),dbinom(18, size = 30, prob = .05),dbinom(19, size = 30, prob = .05),dbinom(20, size = 30, prob = .05),dbinom(21, size = 30, prob = .05),dbinom(22, size = 30, prob = .05),dbinom(23, size = 30, prob = .05),dbinom(24, size = 30, prob = .05),dbinom(25, size = 30, prob = .05),dbinom(26, size = 30, prob = .05),dbinom(27, size = 30, prob = .05),dbinom(28, size = 30, prob = .05),dbinom(29, size = 30, prob = .05),dbinom(30, size = 30, prob = .05))
plot(x,y, xlab = "# of Deaths", ylab = "Probability", main = "Binomial Probability Distribution", col = "green")
## find lambda or mean of scenario
l <- 30*0.05
l
## [1] 1.5
##Poisson Probability
dpois(5, l)
## [1] 0.01411996
##Comparison
dpois(0, l)
## [1] 0.2231302
dpois(1, l)
## [1] 0.3346952
# plotting all outcomes
x <- c(0:30)
z <- c(dpois (0, l),dpois (1, l), dpois (2, l), dpois (3, l), dpois (4, l), dpois (5, l), dpois (6, l), dpois (7, l), dpois (8, l), dpois (9, l), dpois (10, l), dpois (11, l), dpois (12, l), dpois (13, l), dpois (14, l), dpois (15, l), dpois (16, l), dpois (17, l), dpois (18, l), dpois (19, l), dpois (20, l), dpois (21, l), dpois (22, l), dpois (23, l), dpois (24, l), dpois (25, l), dpois (26, l), dpois (27, l), dpois (28, l), dpois (29, l), dpois (30, l))
plot(x,z, xlab = "# of Deaths", ylab = "Probability", main = "Poisson Probability Distribution", col = "red")
