1.Assume Y is a discrete random variable with a mean and a variance of 2, and let X = Y + 1.
a) Do you expect the mean of X to be larger than, smaller than, or equal to ยต = ๐ธ(๐ )? Why?
b) Express ๐ธ(๐) = ๐ธ(๐ + 1) in terms of ยต = E(Y ). Does this result agree with your answer to part (a)?
c) Recalling that the variance is a measure of spread or dispersion, do you expect the variance of X to be larger than, smaller than, or equal to ๐ 2 = ๐(๐ )? Why?
2. In your notes calculate the median and interquartile for Example 3.2.2 and 3.2.3 under Continuous Uniform Distribution notes.
3. Work out the mean and variance of Gamma Distribution.
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