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#---   Classical and Bayesian inference (AMS132)   ---#
#---   Class 1                                     ---#
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#-- remember to use ?function for help on the functions
#   "#" are used to write comments

#-- try uring R as a calculator:
1+1
sqrt(25) # ?sqrt
exp(10) # ?exp
cos(pi) # ?cos
sin(pi) #?sin

#-- the exponential distribution with rate theta:
#   distribution function:
pexp(2, rate=0.5) # ?pexp
curve(pexp(x, 0.5), 0,10)
curve(pexp(x, 0.5), 0,10, xlab="x", ylab="distribution function")

#   probabiity density function:
dexp(2, rate=0.5) # the same as 0.5*exp(-0.5*2) 
curve(dexp(x, 0.5), 0,10, xlab="x", ylab="probability density function")

#   quantile function
qexp(0.9, rate=0.5)
curve(qexp(x, 0.5), 0, 1, xlab="probability", ylab="quantile function")

#   (pseudo) random variable generator
rexp(1, rate=0.5)