53.Suppose that you are given a decision situation with three possible states of nature: S₁, S₂, andprobabilities are P(s₁) = 0.4, P(s₂) = 0.1, and P(s3) = 0.5. With sample information I,P(I|S₁) = 0.1, P(I|s₂) = 0.05, and P(I|s3) = 0.2. Compute the revised or posterior probabilities:P(s₁|I), P(s₂|I), and P(s3|I).Tutorial ExerciseClick here to begin!The prior

Given, The prior probabilities are P(s1) = 0.4 , P(s2) = 0.1 and P(s3) = 0.5 Sample information I,…

Answered: Tutorial Exercise Suppose that you are…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Using the below table: A1 A2 B1 0.4 0.3 B2 0.2 0.1 Compute P(A1 or B1). Compute P(A1 or B2). Calculate the marginal probabilities from the following table of joint probabilities. Determine P(A1 | B1). Determine P(A2 | B1). Did your answers to parts (a) and (b) sum to 1? Is this a coincidence? Explain. Calculate P(A1 | B2). Calculate P(A2 | B1). Are the events independent? Explain
Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: x 1 2 3 4 5 y 15.8 17.3 14.4 19.6 20.0 Σx = 15; Σy = 87.1; Σx2 = 55; Σy2 = 1,540.45; Σxy = 272 (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.) x = y = b = ŷ = + x
3
If the random variable X denotes the real valued outcomes given in the following table with the given frequency of occurrence of each of the outcomes, fill in the last line of the table and find the expected value of X. Outcome -2 -1 0 1 2 Frequency 22 29 18 12 20 P(X) E(X) =
The linear probability model contains heteroskedasticity unless a. all the slope parameters are positive b. all the slope parameters are zero c. the intercept parameter is zero d. the independent variables are binary
USE THE 8-STEP HYPOTHESIS TESTING Refer to the study by Carter et al. [A-9], who investigated the effect of age at onset of bipolar disorder on the course of the illness. One of the variables studied was subjects' family history. Table 3.4.1 shows the frequency of a family history of mood disorders in the two groups of interest: early age at onset (18 years or younger) and later age at onset (later than 18 years). Family History of Mood Disorders Early ≤ 18(E) 28 19 41 53 Later > 18 (L) 35 38 44 60 141 Total 63 57 85 113 Negative (A) Bipolar disorder (B) Unipolar (C) Unipolar and bipolar (D) Total 177 318 Source: Tasha D. Carter, Emanuela Mundo, Sagar V. Parkh, and James L. Kennedy, "Early Age at Onset as a Risk Factor for Poor Outcome of Bipolar Disorder," Journal of Psychiatric Research, 37 (2003), 297-303. Can we conclude on the basis of these data that subjects 18 or younger differ from subjects older than 18 with respect to family histories of mood disorders? Let a = .05.
Spam: A researcher reported that 71.8% of all email sent in a recent month was spam. A system manager at a large corporation believes that the percentage at his company may be 70%. He examines a random sample of 500 emails received at an email server, and finds that 374 of the messages are spam. Can you conclude that the percentage of emails that are spam is greater than 70% ? Use both a=0.10 and a=0.01 levels of significance and the P-value method with the TI-84 Plus calculator. Part: 0/ 4 Part 1 of 4 State the appropriate null and alterņate hypotheses. do O
Hans plays a game when he exercises. He chooses a marble from a bag of three marbles: one is blue, one is red, and one is green. Based on the marble he chooses, he completes a certain number of push-ups, as shown below. Marble Number of push-ups blue red green 10 Consider choosing a marble like sampling from a population. (The population mean of the number of push-ups is u=9.00 and the population standard deyiation is o =0.82.) (a) Suppose a sample of size 2 is randomly selected from the population, with replacement, as follows. One marble is randomly chosen, the number of push- ups is completed, and the marble is put back into the bag. Then for a second time a marble is randomly chosen and the number of push-ups is completed. There are 9 possible samples. The numbers of push-ups for several of the possible samples have been listed in the table below. Enter the numbers of push-ups for the remaining possible samples. When you are done, select "Compute". In the "Sample mean, x" column,…

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