Question 13, page 199. The Poisson distribution with parameter lambda = .3 has been assigned for the outcome of an experiment. Let X be the outcome function. Find P(X = 0), P(X = 1), and P(X > 1)

lambda = 0.3

p_X_eq_0 = exp(-lambda)

p_X_eq_0
## [1] 0.7408182
lambda = 0.3

p_X_eq_1 = lambda*exp(-lambda)

p_X_eq_1
## [1] 0.2222455

Question 3, page 247. In a class there are 20 students: 3 are 5’ 6”, 5 are 5’8”, 4 are 5’10”, 4 are 6’, and 4 are 6’ 2”. A student is chosen at random. What is the student’s expected height?

n = 20

H_5_6 = 3*(5*12+6)
H_5_8 = 5*(5*12+8)
H_5_10 = 4*(5*12+10)
H_6 = 4*6*12
H_6_2 = 4*(6*12+2)

Exp_height = (H_5_6 + H_5_8 + H_5_10 + H_6 + H_6_2)/n

Exp_height/12
## [1] 5.841667

Exp Height = 5’ 10"