## Brief summary of the R commands we've been using when thinking
## about distributions.

# The first letter tells you what you're doing: the two common ones are
# p and q.  Use p to tell you how much of the distribution is below the
# value you are putting in; use q to do the opposite. 

# The main distributions we've been using are normal (norm in R), 
# binomial (binom in R) and t (t in R).  For binomial you need to 
# specify the number of trials and probability of success and for t
# you need to specify the degrees of freedom. They all have extra
# options (see the help commands).   

# So, for example, to find out what proprtion of the normal distribution
# lies below 1.2 (on the "z" axis of the standardised distribution) type

pnorm(1.2)

# To find the same number but when you have a t distribution with 8 degrees
# of freedom rather than a normal distribution use

pt(1.2, 8)

# To go in the other direction and find the z-score that has 45% of the 
# normal distribution below it use

qnorm(0.45)

# Given a binomial experiment with 100 trials and a 3/4 probability 
# of success, where is the point below which 30% of the outcomes fall?

qbinom(0.3, 100, 3/4)