In: Statistics and Probability
Let X be a continuous random variable that has a uniform distribution between 0 and 2 and let the cumulative distribution function F(x) = 0.5x if x is between 0 and 2 and let F(x) = 0 if x is not between 0 and 2. Compute
1. the probability that X is between 1.4 and 1.8
2. the probability that X is less than 1.2
3. the probability that X is more than 0.8
4. the expected value of X
5. the variance of X.