Help in solving the questions in the attachments below.

A discrete random variable X has probability function given by: 0 2 P(X = x) 0.3 0.5 0.2 Calculate: (i) E(X ) (ii) var( X ) (iii) the coefficient of skewness.Show that the variance of a discrete random variable X is given by: var(X ) = G*(1)+G'()-[G'()] where G(r) denotes the probability generating function of X .Write brief notes on the following: (a) Scarcity and choice. (b) Diminishing marginal utility. (c) Price clasticity of demand. (d) Income elasticity of demand. (c) Substitution and income effects of a price change.If the random variable X has a Poisson distribution with mean 1, derive an expression for the expected value of 1/(X + 1). [3]