Let us understand probability density (or mass) functions. If we roll a sixsided dice. the probability mass function is 0, otherwise. 16, ifzr=1,2,3,4,'.6 9(rL')={ / d Then. it is not difcult to see 9(1) 2 1/6 is the probability of getting 1 from the dice. and 29(1):) =1 35:1 because the sum of the probabilities of all outcomes must equal to 1. Let us consider the probability density function of a normal distribution Where its mean is 0 and its standard deviation is 1. It is clear to see that f (0) = 1/x/2 z 0.3989 means the probability that the event :1: = G happens. DC 1. It is known that a single integral / :L'f (:L') dag is the mean of the normal distribution. DO Compute the single integral using the usubstitution