Answer the following questions. Prove your answers using derivations, following the properties of summation operator, expectations operator, and variance operator. 2. Define: (i) A random variable: X...

Extracted text: Answer the following questions. Prove your answers using derivations, following the properties of summation operator, expectations operator, and variance operator. 2. Define: (i) A random variable: X (ii) X has a distribution with mean, H, and variance, o. (iii) A random variable: Y (iv) Y has a distribution with mean, u, and variance, o. (v) A random sample of (X, Y), with a sample size of n