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In: Statistics and Probability

Let X be a continuous random variable that has a uniform distribution between 0 and 2...

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.

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