Part 2. Random Variables 5. Let X be a continuous random variable with probability density function: 0, if f(x) = x < 0 + 0.3x, if 0 x 2 - if x> 2 Find the variance of random variable X. 6. The cumulative distribution function of random variable X is given: 0, F(x)=0.5+0.75x-0.25x, 1 if x -1 if-1 1 Find probability density function and expected value of X. 7.4 black, 5 red and 1 white car are on display in a car shop. A firm orders 3 cars in this shop, and they are randomly chosen from the cars on display. Construct the distribution law of the number of red cars sold to the firm. Indicate the most probable value and its probability. 8. A vaccine takes on average 3 years to develop, the time to development is distributed exponentially. What is the probability that a vaccine will be developed against a certain disease in half a year?