CSE - 571 Homework - 4 (1)

Specifically, it would be helpful to see an illustration of transition probabilities for a zero-recurrence renewal Markov chain.

Singels and system

с с1 c2 c3 c4 xi1 0.4 0.2 0.7 0.0 xi2 0.1 0.1 0.1 0.3 xi3 0.5 0.7 0.2 0.7 -Use the cosine amplitude method to develop the fuzzy relation R that relates the pollution degree to the?

Logistic regression aims to train the parameters from the training set D = {(x(i),y(i)), i 1,2,...,m, y ¤ {0,1}} so that the hypothesis function h(x) = g(0¹ x) 1 (here g(z) is the logistic or sigmod function g(z) can predict the probability of a 1+ e-z new instance x being labeled as 1. Please derive the following stochastic gradient ascent update rule for a logistic regression problem. 0j = 0j + a(y(¹) — hz(x)))x; ave. =

Consider a Diffie-Hellman scheme with a common prime q = 11 and a primitive root α = 2.  Show that 2 is a primitive root of 11. If user A has public key YA = 9, what is A’s private key XA? If user B has public key YB = 3, what is the secret key K shared with A?

Theory of Computation Prove that XY is undecidable XY ​​= { ⟨M⟩ ∣ M is a TM where x∈L(M) and y∈L(M) } Prove this by reducing it from ATM which is proven to be undecidable

Give an example of a random variable X : {b, c, d, e} → N (Natural Number) with expectation 2, where each of {b, c, d, e} has equal probability

Consider the case of a simple Markov Decision Process (MDP) with a discount factor gamma = 1. The MDP has three states (x, y, and z), with rewards -1, -2, 0, respectively. State z is considered a terminal state. In states and y there are two possible actions: a₁ and a2.   The transition model is as follows:   In state x, action a1 moves the agent to state y with probability 0.9 and makes the agent stay put with probability 0.1. In state y, action a1 moves the agent to state with probability 0.9 and makes the agent stay put with probability 0.1. In either state or state y, action a2 moves the agent to state z with probability 0.1 and makes the agent stay put with probability 0.9. Please answer the following questions:                                       Draw a picture of the MDP  What can be determined qualitatively about the optimal policy in states x and y? Apply the policy iteration algorithm discuss in class, showing each step in full, to determine the optimal policy and the…

Q-1. Consider the Farmer-Wolf-Goat-Cabbage Problem described below: Farmer-Wolf-Goat-Cabbage Problem There is a farmer with a wolf, a goat and a cabbage. The farmer has to cross a river with all three things. A small boat is available to cross the river, but farmer can carry only one thing with him at a time on the boat. In the absence of farmer, the goat will eat the cabbage and wolf will eat the goat. How can the farmer cross the river with all 3 things? State Space Formulation of the Problem State of the problem can be represented by a 4-tuple where elements of the tuple represent positions of farmer, wolf, goat and cabbage respectively. The position of boat is always same as the position of farmer because only farmer can drive the boat. Initial state: (L, L, L, L) Operators: 1.      Move farmer and wolf to the opposite side of river if goat and cabbage are not left alone. 2.      Move farmer and goat to the opposite side of river. 3.      Move farmer and cabbage to the opposite…

Determine the causality for each of the following linear systems. a. y(n) = 0.5x(n) + 20x(n − 2) – 0.1y(n-1) b. y(n) = x(n + 2) - 0.4y(n-1) c. y(n) = x(n - 1) + 0.5y(n + 2)

Bayes Nets Probability and Inference

The following MDP world consists of 5 states and 3 actions: (1, 1) (1, 2) Action: Exit - -10 Actions: down, right (2, 1) (2, 2) Action: Exit = -10 Actions: down, right (3, 1) Action: Exit = 10 When taking action down, it is successful with probability 0.7. with probability 0.2 you go right, and with probability 0.1 you stay in place. When taking action right, it is successful with probability 0.7, with probability 0.2 you go right, and with probability O.1 you stay in place. When taking action Exit, it is successful with probability 1.0. The only reward is when taking action Exit, and there is no discounting. Calculate the value of states using Value Iteration algorithm for required time step: Provide the value for State (1,2) at time step 4 (calculate to 3 decimal places): Va(1,2) =

#3

The following is an illustration of the one-step transition probabilities for a renewal Markov chain with no recurrence.

(a) Assume a probabilistic model is represented by the Bayesian network (I) in Figure 3. Is it then always possible to represent the model instead with the Bayesian network (I) of Figure 32 Given an argument for your answer. (b) Assume a probabilistic model is represented by the Markov network (III) in Figure 3. Is it then always possible to represent the model instead with the Bayesian network (1) of Figure 3? Given an argument for your answer. (1I) (II) (1)

True or False. Explain a. It is quite common to experience an unbounded divergence when we use the deadly triad in Deep Q-Learning: bootstrapping, value function approximation, and off-policy learning. b. As the size of an MDP (i.e., the number of states or actions) increases, an RL agent is required to store more weight parameters for the linear function approximation of the value function.

Correct answer will be upvoted else downvoted. Computer science.    in case there are two planes and a molecule is shot with rot age 3 (towards the right), the cycle is as per the following: (here, D(x) alludes to a solitary molecule with rot age x)    the primary plane delivers a D(2) to the left and lets D(3) progress forward to the right;    the subsequent plane delivers a D(2) to the left and lets D(3) progress forward to the right;    the primary plane lets D(2) forge ahead to the left and creates a D(1) to the right;    the subsequent plane lets D(1) progress forward to one side (D(1) can't create any duplicates).    Altogether, the last multiset S of particles is {D(3),D(2),D(2),D(1)}. (See notes for visual clarification of this experiment.)    Gaurang can't adapt up to the intricacy of the present circumstance when the number of planes is excessively huge. Help Gaurang find the size of the multiset S, given n and k.    Since the size of the multiset can be extremely huge, you…

Correct and detailed answer will be Upvoted. Thank you

No. 3 By natural deduction, show the validity of Jx (P(x) A Q(x)), Vy (P(x) → R(x)) (R(x) A Q(x)).

Consider a Diffie-Hellman scheme with a common prime q = 17 and a primitive root α = 3. a) If user A has a private key XA=4, what is A’s public key, YA? b) A sends YA to B. If B has a private key XB=6, what is the shared secret key, K that B can calculate and share with A? c) If B computes YB and sends it to A, what is the shared secret Key, K computed by A?

3. In your local nuclear power station, there is an alarm that senses when a temperature gauge exceeds a given threshold. The gauge measures the temperature of the core. Consider the Boolean variables A (alarm sounds), FA (alarm is faulty), and FG (gauge is faulty) and the multivalued nodes G (gauge reading) and T (actual core temperature). a. Draw a Bayesian network for this domain, given that the gauge is more likely to fail when the core temperature gets too high. b. Is your network a polytree? Why or why not?

Let M be the PDA defined by Q = {q, q0 , q1 , q2}, Σ = {a,b}, Γ = {a}, F := {q , q1}.δ(q0 , a , Z0) = {(q, Z0 ) } δ(q , a, Z0) = {(q , aZ0)} δ(q , a, a) = {(q , aa)} δ(q , b , a) = {(q1 ,e)} δ(q1 , b , a) = {(q1 ,e)} δ(q1 , b, Z0 ) = {(q2 , e)} Describe the CFG and the language accepted by M

Algorithm A search using the heuristic h(n) = a for some fixed constant a > 0 is guaranteed to find an optimal solution Select one: True False The Perceptron Learning Rule is a sound and complete method for a Perceptron to lear correctly classify any 2-class classification problem Select one: True False systems are Data-driven, where as systems are goal-driven. Select one: a. Backward Chaining & Forward Chaining b. Forward Chaining & Backward Chaining c. Spanning Chaining & Backward Chaining d. None of the above it is a search algorithm that requires less memory Select one: a. Breadth-First Search b. Linear Search c. Optimal Search d. Depth First Search Rationality is? Select one: a. being reasonable b. being sensible c. having good sense of judgment d. All of the above Breadth-first search is similar to minimax search Select one: True False

The room temperature x in Fahrenheit (F) is converted to y in Celsius (C) through the function y = f(x) = 5(x-32)/9. Let a fuzzy set B1 (in Fahrenheit) be defined by B1 = 0.15/76 + 0.42/78 + 0.78/80 + 1.0/82 + 1.0/84 What is the induced fuzzy set of B1 in terms of the extension principle? B2 = ?

A Probabilistic Model for Approaching the Selection Pressure Curve