3.5

#1a
lambda <- 40/10  # 4
dpois(3, lambda)

[1] 0.1953668

#1b
1 - ppois(4, lambda)

[1] 0.3711631

#1c
qpois(0.5, lambda)

[1] 4

#1d
sim <- rpois(10000, lambda)
mean(sim == 3)

[1] 0.1938

mean(sim >= 5)

[1] 0.3777

median(sim)

[1] 4

#8c
lambda <- 0.8
p_odd <- (1 - exp(-2*lambda)) / 2
p_odd

[1] 0.3990517

sim <- rpois(10000, lambda)
mean(sim %% 2 == 1)

[1] 0.406