1. Check that this is a probability density function. Then calculate the mean and the standard deviation. (8) 3 P(I) = 14 ( I' + I ) I E [0, 2] 2. Check that this is a probability density function. Then calculate the mean and the standard deviation. (8) P(I)= I E [1, 00) 3. Probability density functions describe the probability of certain measurements. The maximum probability is 1; an event or measurement with probability 1 is certain to happen. Explain how the probability density function itself can have values larger than 1 and still work to calculate probability. (3)