Answer to Question #229744 in Statistics and Probability for Sne

Question

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 µ = 𝐸(𝑌 )? Why?

b) Express 𝐸(𝑋) = 𝐸(𝑌 + 1) in terms of µ = 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 𝜎 2 = 𝑉(𝑌 )? 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.