Consider a game where you need to fill a 5-digit number by spinning a wheel. Every time you spin the wheel a random digit shows up between 0 – 9 with equal probability. You are to decide where to place the digit in your number. Once you choose a location for the digit you cannot change it. Your objective is to maximize the number you get. (a) Set this up as a Markov Decision Process, identify the states, actions, and transition matrices.

Either a mixed column or mixed row strategy is given. Use the given payoff matrix and find the optimal pure strategy (or strategies) the other player should use. Express the answer as a row or column matrix. Also determine the resulting expected payoff.

↑ The 1990 census reported that 32% of the households in Middletown were homeowners and the remainder were renters. During the next decade, 10% of the homeowners became rent and the rest continued to be homeowners. Similarly, 14% of the renters became homeowners and the rest continued to rent (A) Fill in the appropriate transition matrix for this process. Homeowners Homeowners Renters Renters AR NE

Valve A: 92% Valve B: 94% Valve C: 93%

Class Exercise 1: Players I and II simultaneously call out one of the numbers one or two. Player I's name is Odd; he wins if the sum of the numbers is odd. Player Il's name is Even; she wins if the sum of the numbers is even. The amount paid to the winner by the loser is always the sum of the numbers in rands. Set up the payoff matrix.

A car wash has three different types of washes: basic, classic, and ultimate. Based on records, 45% of customers get the basic wash, 35% get the classic wash, and 20% get the ultimate wash. Some customers also vacuum out their cars after the wash. The car wash records show that 10% of customers who get the basic wash, 25% of customers who get the classic wash, and 60% of customers who get the ultimate wash also vacuum their cars. The probabilities are displayed in the tree diagram.What is the probability that a randomly selected customer purchases the basic or classic car wash if they vacuum their car?A) 0.13B) 0.48C) 0.52D) 0.80