Question: It is stated that if all variables in a Bayesian network are binary, the probability distribution over some variable X with n parents PaX

It is stated that if all variables in a Bayesian network are binary, the probability distribution over some

It is stated that if all variables in a Bayesian network are binary, the probability distribution over some variable X with n parents PaX can be represented by 2n independent parameters. Imagine that X is a binary variable with two parent variables that are not necessarily binary. Imagine that the first parent can assume three different values and that the second can assume two values. How many independent parameters are needed to represent this distribution (P(XPaX) How many would it be if you added another parent that can assume four different values? Now assume that X itself is not binary but can assume three different values (and still has the three parents as specified above). How many values are needed to represent this distribution? Can you come up with a general rule for the number of independent parameters needed to represent a distribution over some variable X with parents Pa?

Step by Step Solution

★★★★★

3.34 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

media pointerfileservicefileHTUFFm5Sw... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

How many hex digits are needed to represent a memory address for a PC that uses 20-bit address code for its memory location?

How many arithmetic operations are needed to perform k steps of the Jacobi iteration? What about Gauss-Seidel? Under what conditions is Jacobi or Gauss-Seidel more efficient than Gaussian Elimination?

How many arithmetic operations are needed to implement one iteration of the conjugate gradient method? How many iterations can you perform before the method becomes more work that direct Gaussian...

In Example 3 it is stated that for all x we have | sin x| |x|. Use the following to verify this statement. a. Show that for all x 0we have f (x) = xsin x is non-decreasing, which implies that sin x...

Assume you have just been hired as business manager of PizzaPalace, a pizza restaurant located adjacent to campus. The company's EBIT was $500,000 last year, and since the university's enrollment is...

Now calculate the corporate value. Assume you have just been hired as a business manager of PizzaPalace, a regional pizza restaurant chain. The companys EBIT was $50 million last year and is not...

What does this example illustrate about the impact of financial leverage on ROE? Assume you have just been hired as a business manager of PizzaPalace, a regional pizza restaurant chain. The companys...

Assume you have just been hired as business manager of PizzaPalace, a pizza restaurant located adjacent to campus. The companys EBIT was $500,000 last year, and since the universitys enrollment is...

Now, to develop an example that can be presented to PizzaPalaces management to illustrate the effects of financial leverage, consider two hypothetical firms: Firm U, which uses no debt financing, and...

What does capital structure theory attempt to do? What lessons can be learned from capital structure theory? Be sure to address the MM model. Assume you have just been hired as business manager of...

This is written and solved ONLY using rStudio. But if you have an easier way to do it, that works: Information related to questions: For this exercise, we are going to look at salaries for college...

Carla Company began operations on January 2, 2019. It employs 11 individuals who work 8-hour days and are paid hourly. Each employee earns 9 paid vacation days and 7 paid sick days annually. Vacation...

TAC Industries Inc. sells heavy equipment to large corporations and federal, state, and local governments. Corporate sales are the result of a competitive bidding process, where TAC competes against...

Suppose there is sudden increase in preference of chocolates. But the cost of production rises due to rise in the price of milk. Use a demand supply model, to determine what happens to the...

Which of the following does NOT illustrate how deviant behavior can impact a company? Employees don't feel safe. The company could face a lawsuit. The company's workforce is unaffected. It may limit...

In the figure below, we see that traditional one-person-one-vote (1p1v) majority voting results in an inefficient majority "yes" vote (two in favor, one opposed). Let's see whether the outcome is...

Following are the transactions of a new company called Pose-for-Pics. Aug. 1 Madison Harris, the owner, invested $6,250 cash and $26,875 of photography equipment in the company in exchange for common...

Match each of the key terms with the definition that best fits it. _______________ A record of the sequence of data entries and the date of those entries. Here are the key terms from the chapter. The...

In his letter of August 24, 1654, Pascal was trying to show how a pot of money should be allocated when a gambling game must end prematurely. Imagine a game where each turn consists of the roll of a...

Construct levels 0, 1, and 2 of the planning graph for the problem in Figure 10.1. Figure 10.1 Init(At (1, SFO) At(>, JFK) At(P, SFO) At(>, JFK) go (C) argo(C>) ^ Plane (P.) Plane(P:) Aiport...

Consider the Allais paradox described : an agent who prefers B over A (taking the sure thing), and C over D (taking the higher EMV) is not acting rationally, according to utility theory. Do you think...

3. As an interviewer, what is the best way to ask questions that will get an interviewee to tell you about what motivates him or her?

Where do you see yourself in the future?

1. What type of outfits are you expected to wear at work?