Paramedics in a small town can be sent on as many as 6 calls during one shift of work. The following table shows the probability distribution of the random variable X, the number of calls a paramedic is sent on during a shift of work.

x. 0. 1. 2. 3. 4. 5. 6.

f(x)0.02 0.08 0.13 0.22 0.37 0.12 0.06

(a) Find the cumulative distribution function (the cdf), F(x), for the random variable X. Show your calculations for each probability.

(b) What is the probability that a paramedic will be sent on at most 4 calls in a particular shift if it is a shift where they are sent on at least one call?

(c) Find (2+3)E(X2+3).

Can you explain how to do a b and c?