normal_binom_distribution.R

#normal distribution examples
#computing normal probabilities with R

#calculate P(Z <--2.0785)
pnorm(q = -2.0785, mean = 0, sd=1)

#calculate P(x <= 10) for X ~ N(7.1429, 6.1224)
pnorm(q=2, mean=50/7, sd= sqrt(300/49))


#natural births on a monday problem
#use R to calculate P(Y<=2)
pbinom(q=2, size=50, prob=1/7)

#use R to calculate P(X<=2) for X ~ N(50/7, 300/49)
pnorm(q=2, mean=50 / 7, sd=sqrt(300/49))


#probability that more than 2 but fewer than 10 of the 50 births occur on a monday
#calculate P(x < 9.5) - P(X < 2.5) for the previous x mean and variance values
pnorm(q=9.5, mean=50/7, sd= sqrt(300/49)) -
pnorm(q=2.5, mean=50/7, sd=sqrt(300/49))


#added tutorial questions
dbinom(x=8, size=10, prob=0.7)


#P (x < 3)
pbinom(q=3, size=10, prob=0.7)

#cumulative function for more than 1 X value
pnorm(q = -2, mean=0, sd=1, lower.tail = F)
pnorm(q=0.4, mean=0, 1, lower.tail = F)


#exact probability of P(X<=100)
pbinom(50, size=3000, prob=0.02)


#normal approximation
pnorm(-1.304)



#n = 30, p = 0.05, 
#calculate probability that 3 animals are caught in these 30 traps for a given week
dbinom(x=3, size=30, prob = 0.05)

#calculate and find when P(Y<3)
pbinom(q=2, size=30, prob=0.05)