## uniform distribution

runif(1, 5,15)
runif(1, 5,15)
runif(1, 5,15)
runif(1, 5,15)
runif(1, 5,15)

runif(100, 5,15)

x = runif(100, 5,15)
hist(x)

hist(runif(100, 5, 15))
hist(runif(100, 5, 15))
hist(runif(100, 5, 15))
hist(runif(100, 5, 15))
hist(runif(100, 5, 15))

hist(runif(1000, 5, 15))
hist(runif(10000, 5, 15))
hist(runif(100000, 5, 15))
hist(runif(1000000, 5, 15))

## normal distribution

hist(rnorm(1000))
hist(rnorm(1000, 0, 1))
hist(rnorm(10000, 0, 1))
hist(rnorm(100000, 0, 1))

?rnorm # help

pnorm(1.96) # P(Z<1.96)
dnorm(1.96) # density
qnorm(.975) # z0 such that P(Z<z0)=0.975

curve(dnorm(x, 0, 1), -4, 4)
curve(pnorm(x, 0, 1), -4, 4)

## xxx
curve(dnorm(x, 0, 1), -4, 4)
curve(dnorm(x, 1, 1), -4, 4, add=TRUE, col='red')
curve(dnorm(x, 0, 2), -4, 4, add=TRUE, col='blue')

hist(rnorm(1000, 0,1), prob=TRUE)
curve(dnorm(x, 0, 1), add=TRUE)

## Gamma distribution

?dgamma # to see why you want to use 'scale=' option explicitly

## xxx
curve(dgamma(x, 1, scale=1), 0, 10)
curve(dgamma(x, 2, scale=1), 0, 10, add=TRUE)
curve(dgamma(x, 4, scale=1), 0, 10, add=TRUE)
curve(dgamma(x, 2, scale=2), 0, 10, add=TRUE, col='red')

hist(rgamma(1000, 4,scale=1), prob=TRUE)
curve(dgamma(x, 4, scale=1), 0, 10, add=TRUE)

## Exponential xxx
curve(dgamma(x, 1, scale=1), 0, 10)
curve(dgamma(x, 1, scale=2), 0, 10, add=TRUE)
curve(dgamma(x, 1, scale=3), 0, 10, add=TRUE)

## Chi-squared xxx
curve(dgamma(x, 1/2, scale=2), 0, 10) # 1 d.f.
curve(dgamma(x, 2/2, scale=2), 0, 10, add=TRUE) # 2 d.f.
curve(dgamma(x, 3/2, scale=2), 0, 10, add=TRUE) # 3 d.f.

## Beta distribution xxx
curve(dbeta(x,5,3), 0,1)
curve(dbeta(x,3,3), 0,1, add=TRUE, col='red')
curve(dbeta(x,2,2), 0,1, add=TRUE, col='blue')