Problem 1. Consider a random variable X which has the distribution with the following prob- ability density function: PCT) (a) Find the value 33(1). Hint: nd it from the condition that the total probability is 1. (b) Find P(X %), P(|X 1| 5 g), (c) Draw the graph of the cumulative distribution function of X. Problem 2. Consider a random variable X which has the distribution with the following prob- ability density function: 19(3) 0.5 (a) Show that the total probability is 1. (b) Find P(X g 2), P(2 g X g 3). (c) Draw the graph of the cumulative distribution function of X