A bag contains five balls numbered from 1 to 5. Another bag contains three balls numbered from 1 to 3. A ball is drawn randomly from each bag and the numbers on the two balls are summed up to find the final outcome. This final outcome is denoted with a random variable X.
a) Give the range space for X.
b) Find P(X=xi) probabilities for all possible outcomes, and plot the probability mass function (pmf) of X.
c) Plot the cumulative distribution function (cdf) of X. What is the value of P(X≤3.65)?