# Question: Let us examine the behavior of the variance update in Equation

Let us examine the behavior of the variance update in Equation (15.1).

a. Plot the value of σ2t as a function of t, given various values for σ2x and σ2z.

b. Show that the update has a fixed point u σ2 such that σ2t →, σ2 as t →∞ and calculate the value of σ2

c. Give a qualitative explanation for what happens as σ2x → 0 and σ2z → 0.

a. Plot the value of σ2t as a function of t, given various values for σ2x and σ2z.

b. Show that the update has a fixed point u σ2 such that σ2t →, σ2 as t →∞ and calculate the value of σ2

c. Give a qualitative explanation for what happens as σ2x → 0 and σ2z → 0.

## Answer to relevant Questions

Show how to represent an HMM as a recursive relational probabilistic model, as suggested in Section 14.6.Tickets to a lottery cost $1. There are two possible prizes: a $10 payoff with probability 1/50, and a $1,000,000 payoff with probability 1/2,000,000. What is the expected monetary value of a lottery ticket? When (if ever) ...For either of the airport-sitting diagrams from Exercises 16.8 and 16.9, to which conditional probability table entry is the utility most sensitive, given the availableevidence?Sometimes MDPs are formulated with a reward function R(s, a) that depends on the action taken or a reward function R (s, a, s’) that also depends on the outcome state.a. Write the Bellman equations for these ...Repeat Exercise 18.1 for the case of learning to play tennis (or some other sport with which you are familiar) is this supervised learning or reinforcement learning?Post your question