Bayesian Methods 9.9 Zeros on a Roulette Wheel: We now wish to make a more sophisticated...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Bayesian Methods 9.9 Zeros on a Roulette Wheel: We now wish to make a more sophisticated estimate of the number of zeros on a roulette wheel without looking at the wheel. We will do so with Bayesian inference. Recall that when a ball on a roulette wheel falls into a non-zero slot, odd/even bets are paid; when it falls into a zero slot, they are not paid. There are 36 non-zero slots on the wheel. We assume that the number of zeros is one of {0, 1, 2, 3}. We assume that these cases have prior probability {0.1,0.2, 0.4, 0.3}. (a) Write n for the event that, in a single spin of the wheel, an odd/even bet will not be paid (equivalently, the ball lands in one of the zeros). Write z for the number of zeros in the wheel. What is P(n|z) for each of the possible values of z (i.e. each of {0, 1, 2, 3})? (b) Under what circumstances is P(z = 0|observations) NOT 0? (c) You observe 36 independent spins of the same wheel. A zero comes up in 2 of these spins. What is P(z|observations)? Bayesian Methods 9.9 Zeros on a Roulette Wheel: We now wish to make a more sophisticated estimate of the number of zeros on a roulette wheel without looking at the wheel. We will do so with Bayesian inference. Recall that when a ball on a roulette wheel falls into a non-zero slot, odd/even bets are paid; when it falls into a zero slot, they are not paid. There are 36 non-zero slots on the wheel. We assume that the number of zeros is one of {0, 1, 2, 3}. We assume that these cases have prior probability {0.1,0.2, 0.4, 0.3}. (a) Write n for the event that, in a single spin of the wheel, an odd/even bet will not be paid (equivalently, the ball lands in one of the zeros). Write z for the number of zeros in the wheel. What is P(n|z) for each of the possible values of z (i.e. each of {0, 1, 2, 3})? (b) Under what circumstances is P(z = 0|observations) NOT 0? (c) You observe 36 independent spins of the same wheel. A zero comes up in 2 of these spins. What is P(z|observations)?
Expert Answer:
Answer rating: 100% (QA)
a Write n for the event that in a single spin of the wheel an odd even bet will not be paid equ ival ... View the full answer
Related Book For
Posted Date:
Students also viewed these accounting questions
-
Make an order-of-magnitude estimate of the number of revolutions through which a typical automobile tire turn s in 1 yr. State the quantities you measure or estimate and their values.
-
Make a rough estimate of the number of PCS micro cells 100 m in diameter it would take to cover San Francisco (120 square km).
-
Give a big-O estimate of the number of operations (comparisons and additions) used by Floyd's algorithm to determine the shortest distance between every pair of vertices in a weighted simple graph...
-
import java.util.ArrayList; import java.util.Map; import java.util.Set; import java.util.TreeMap; /* * * This class contains a map of string keys, representing professors, to an array list of...
-
At lunch one day, the topic of XBRL is mentioned. One of your colleagues says, It has something to do with schemas, linkbases, and taxonomiesthat is all I know. Then he turns to you and asks, What do...
-
Which x satisfies both |x 3| < 2 and |x 5| < 1?
-
Solve Example 7.15 using the Tsai-Hill criterion instead of the maximum stress criterion. That is, determine the largest torque \(T\) that can be transmitted by the shaft without failure, according...
-
A company with no inventory buys the following three inventory items: On January 10, the company sells one item for $10. On January 15, the company sells a second item $10. The company uses a...
-
1. Write the title of the case and the bibliographic record 2. Mention the parties involved in the case, duly identified as plaintiffs or defendants, etc. 3. What is the main controversy that arises...
-
Fenton Ltd is a manufacturing organisation supplying specialised engineered products to a wide range of public and private sector throughout the UK. You are a trainee in the finance office recently...
-
What social need is fulfilled by the establishment of an urban garden. Use the market failure approache (externalities, public goods, imperfect information, etc) to justify. Details: your local...
-
An object of inertia \(m_{1}\) moving at \(v_{1 i}\) collides elastically with an object of inertia \(m_{2}\) initially at rest. Show that the following solution for the final velocities of the two...
-
Prove that, if s ( X ) s ( X ) is a martingale, then, equality (5.3.3) holds. P x ( T a < T b ) = s ( x ) s ( b ) s ( a ) s ( b ) (5.3.3) (5.3.3) P x ( T a < T b ) = s ( x ) s ( b ) s ( a ) s ( b...
-
At separation distance \(r_{1}\), charged Ping-Pong balls \(A\) and \(B\) repel each other with an electric force of magnitude 0. 40 N. At separation distance \(r_{2}\), charged Ping-Pong balls...
-
A piece of tape is pulled from a spool and lowered toward a \(100-\mathrm{mg}\) scrap of paper. Only when the tape comes within \(8.0 \mathrm{~mm}\) is the electric force magnitude great enough to...
-
A plastic spring with spring constant \(k=450 \mathrm{~N} / \mathrm{m}\) has a relaxed length of \(0.100 \mathrm{~m}\). The spring is positioned vertically on a table, and a charged plastic...
-
The adjusted trial balance of Karise Repairs on December 3 1 follows. \ table [ [ Number , \ table [ [ KARISE REPAIRS ] , [ Adjusted Trial Balance ] , [ December 3 1 ] ] , Debit,,Credit ] , [ 1 0 1 ,...
-
Write a paper by answer the following question: Should Recycling Be Mandatory?
-
A g ray photon emitted by 226 88 Ra has an energy of 0.186 MeV. Use conservation of linear momentum to calculate the recoil speed of a 226 88 Ra nucleus after such a g ray is emitted. Assume that the...
-
A friend tells you that when he takes off his eyeglasses and holds them 23 cm above a printed page the image of the print is erect but reduced to 0.67 of its actual size. (a) Is the image real or...
-
In an Internet video an athlete launches a basketball from a stadium platform that is 16.2 m higher than the hoop. He makes the basket by launching the ball at an angle of 14.5 above horizontal with...
-
LDDS continued to publicly report increasing profits and sales in the financial statements, which allowed it to acquire more companies with no limit to the growth of its stock price. True/False
-
LDDS suffered from high fixed costs coupled with a lack of technical knowledge and expertise in optimizing the configuration of circuits, which resulted in high line costs. True/False
-
WorldCom overstated its earnings by improper accounting for multiple element contracts. True/False
Study smarter with the SolutionInn App