Find X, (the probability distribution of the system after two observations) for the distribution vector X, and the transition matrix T. 0.25 0.1 0.1 0.2 Xo = | 0.60 T=| 0.8 0.7 0.4 0.15 0.1 0.2 0.4 X2 =

Find the stable distribution for the regular stochastic matrix.   0.5 0.2 0.3 0.4 0.7 0.7 0.1 0.1 0 Find the stable distribution.         ​(Type integers or decimals rounded to three decimal places as​ need

A firm's revenue R is stochastically related to the effort exerted by its employee. Effort is a continuous variable. The employee can choose any level of effort e E [0, ). The choice of effort affects revenue so that: E(R|e) = e and Var(R|e) = 1 %3D where E(R|e) and V ar(R|e) denote the expected value and variance, respectively, of rev- enue when the employee exerts effort level e. The employer cannot observe the level of effort exerted by the employee. The employer wants to design a wage contract w based on the revenue and considers only contracts of the form: w-α+ βR and so the employee is guaranteed a payment a and then a bonus payment ßR which de- pends on revenue. The employee is a risk-averse expected utility maximiser. A contract w gives expected utility: Eu(w\e) = E(w\e)-eV ar(w]e) – c(e) where E(wle) and Var(wle) denote the expected value and variance of the contract, re- spectively, conditional on effort e, p is a parameter of risk aversion, and c(e) denotes the disutility of…

Find the marginal probabilities of each random variable X and Y in thefollowing table:- Compute the covariance and the correlation of these two random variables.