Question: Consider a single Boolean random variable Y (the classification). Let the prior probability P(Y = true) be . Lets try to find , given a

Consider a single Boolean random variable Y (the “classification”). Let the prior probability P(Y = true) be π. Let’s try to find π, given a training set D = (y₁, . . . , y_N ) with N independent samples of Y . Furthermore, suppose p of the N are positive and n of the N are negative.

By differentiating the log likelihood L, find the value of π that maximizes the likelihood.

Step by Step Solution

★★★★★

3.25 Rating (146 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Calculation Let the class be Y true The main effect is the classification of a sample The classimputation is the mean value of an Nclass distribution which we assume to be pY 1 05 and nY 1 025 The err... 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 Accounting Questions!

Consider independent random samples from two populations that are normal or approximately normal, or the case in which both sample sizes are at least 30. Then, if Ï1 and Ï2 are unknown but...

Suppose that independent random samples of size n from two normal populations with the known variances Ï21 and Ï22 are to be used to test the null hypothesis µ1 µ2 = t against...

Let y be a binomial random variable with n = 10 and p = .5. a. Calculate P(4 y 6). b. Use a normal approximation without the continuity correction to calculate the same probability. Compare your...

Let X be a random variable with the following probability distribution:

Consider a random variable with the following probability distribution: P(X = 0) = 0.1, P(X = 1) = 0.2, P(X = 2) = 0.3, P(X = 3) = 0.3, and P(X = 4) = 0.1. a. Find P(X 2) b. Find P(1

A random variable follows the normal probability distribution with a mean of 80 and a standard deviation of 20. What is the probability that a randomly selected value from this population a. Is less...

A random variable follows the normal probability distribution with a mean of 124 and a standard deviation of 27. What is the probability that a randomly selected value from this population a. Is...

With reference to Exercise 5.52, find the probability that the random variable will take on a value less than 5. Data From Exercise 5.52 5.52 If a random variable has the gamma distribution with = 2...

Find the value of kurtosis for a vibration amplitude that can be approximated as a discrete random variable with the following probability mass function: x (mm) f(x) 32 -8 2 3 32 5 10 9 16 36 66 36 3...

A random variable follows the normal probability distribution with a mean of 124 and a standard deviation of 27. What is the probability that a randomly selected value from this population a. is...

When vendor invoice is received, Eliana compares it to the purchase order and receiving report for both accuracy and appropriateness of the expenditure. She then records the transaction in the...

For the circuit shown in Fig. 12-47, (a) Obtain the voltage transfer function Hu(w) (b) Find the frequency at which the function is real. + V ww R R Fig. 12-47 F V

Write the phasor equation for the single-loop, coupled circuit shown in Fig. 14-38. j5 . | 1 k = 0.65 10 0 50/0 V j3 K -j8 .

From the following data for a particular period, compute sales and profit variances: Budgeted sales: Actual sales: X, 3,000 units @ Y, 2,000 units @ X, 4,000 units @ Y, 2,500 units @ 20 (standard...

Everly Healthcare has just borrowed $1,000,000 on a five-year, annual payment term loan at a 15 percent rate. The first payment is due one year from now. Construct the amortization schedule for this...

Develop a Gantt chart with the following information. What is the expected duration of the project? What is the critical path? Activity Expected Duration Predecessors A BL 12 8 None None C 5 None D...

Problem 20-5A Gutierrez Company has four operating divisions. During the first quarter of 2014, the company reported aggregate income from operations of $203,500 and the following divisional results....

If the annual fixed costs are 54,000 dinars, the occupation expense represents 20%, the contribution margin is 25%, and the unit selling price is 40 dinars. Required: Calculate the closing point of...

Let A and B be two events defined on S. If the probability that at least one of them occurs is 0.3 and the probability that A occurs but B does not occur is 0.1, what is P (B)?

An apartment building has eight floors. If seven people get on the elevator on the first floor, what is the probability they all want to get off on different floors? On the same floor? What...

A commercial film processor is experimenting with two kinds of fully automatic color developers. Six sheets of exposed film are put through each developer. The number of flaws on each negative...

For the data in Exercise 1, In Exercise 1 A student takes a census of her statistics class and finds that of the 120 students in the class, 25 were born in winter, 35 in spring, 32 in summer, and 28...

Would it be wise for the administrators at the college described in Exercise 1 to conclude that lowering their admission rate (i.e., making it harder to get in) would help to increase their...

We looked at data from the National Oceanic and Atmospheric Administration about their success in predicting hurricane tracks. On the following page is a scatter plot of the error (in nautical miles)...