An urn contains three red balls and four black ones. The two balls are drawn at random (without replacement). The random variable X is the number of red balls among the balls drawn during our experiment.
a) What are the possible values of X?
b) For each possible value of X, determine its probability.
c) Present the distribution law (the probability mass function) of the random variable X as a table.
d) Depict the probability mass function of X as a bar graph.
e) Calculate the mathematical expectation of X.
f) Calculate the variance of X and the standard deviation of X.
g) Calculate the cumulative distribution function of X.