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Example 5.5. Recall Example 5.2 (section 5.1.2). Now, suppose that the Xis will not be directly observable. Instead, we will only be able to observe whether X>0 or X = 0. For example, drivers may not want to reveal to an insurance company that they've had a number of accidents in the past for this will surely increase their premium, but, to mitigate the risk of the insurance industry, government reg- ulations may require that they have to reveal something. So a compromise is reached to balance privacy and transparency-drivers must reveal whether they've had any accident at all (i.e. whether X; > 0 or X; = 0), although they need not reveal exactly how many they've had. Perhaps somewhat surprisingly, we can still estimate the parameter 0 in this case, despite the added complication! The key insight here is that we can define another (fully observable) random variable, 1, X; > 0, Y₁ = 0, X = 0. Recall Example 5.5 (section 5.3). Use the likelihood ratio to find a 95% confidence interval for theta based on data in Table 5.1 ~ Then, Y; Binomial(1, pi), where = Pi P(Y - 1) = P(X; > 0) = 1 - P(X = 0) = e -Ovi (Ovi)º = 1. = 1 − e−vi 0! Table 5.1 Number of individuals (out of 40) who had zero (X; = 0) or at least one (X; > 0) incident, along with their level of activity (v;) One + Vi (X; > 0) Zero (X = 0) Text 8 10 Text 0 4 2 1 873 2 Recall Example 5.5 (section 5.3). Use the likelihood ratio to find 3 7 a 95% confidence interval for theta based on data in Table 5.1 Source: authors.

Example 5.5. Recall Example 5.2 (section 5.1.2). Now, suppose that the Xis will not be directly observable. Instead, we will only be able to observe whether X>0 or X = 0. For example, drivers may not want to reveal to an insurance company that they've had a number of accidents in the past for this will surely increase their premium, but, to mitigate the risk of the insurance industry, government reg- ulations may require that they have to reveal something. So a compromise is reached to balance privacy and transparency-drivers must reveal whether they've had any accident at all (i.e. whether X; > 0 or X; = 0), although they need not reveal exactly how many they've had. Perhaps somewhat surprisingly, we can still estimate the parameter 0 in this case, despite the added complication! The key insight here is that we can define another (fully observable) random variable, 1, X; > 0, Y₁ = 0, X = 0. Recall Example 5.5 (section 5.3). Use the likelihood ratio to find a 95% confidence interval for theta based on data in Table 5.1 ~ Then, Y; Binomial(1, pi), where = Pi P(Y - 1) = P(X; > 0) = 1 - P(X = 0) = e -Ovi (Ovi)º = 1. = 1 − e−vi 0! Table 5.1 Number of individuals (out of 40) who had zero (X; = 0) or at least one (X; > 0) incident, along with their level of activity (v;) One + Vi (X; > 0) Zero (X = 0) Text 8 10 Text 0 4 2 1 873 2 Recall Example 5.5 (section 5.3). Use the likelihood ratio to find 3 7 a 95% confidence interval for theta based on data in Table 5.1 Source: authors.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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Use the likelihood ratio to find
a 95% confidence interval for theta based on data in Table 5.1. Please look at this message and solve my question accordingly, don't just explain the images, I know what's going on in them. The past 2 times I've asked, no one's read my message. 

Example 5.5. Recall Example 5.2 (section 5.1.2). Now, suppose that the Xis will not be directly observable. Instead, we will only be able to observe whether X>0 or X = 0. For example, drivers may not want to reveal to an insurance company that they've had a number of accidents in the past for this will surely increase their premium, but, to mitigate the risk of the insurance industry, government reg- ulations may require that they have to reveal something. So a compromise is reached to balance privacy and transparency-drivers must reveal whether they've had any accident at all (i.e. whether X; > 0 or X; = 0), although they need not reveal exactly how many they've had. Perhaps somewhat surprisingly, we can still estimate the parameter 0 in this case, despite the added complication! The key insight here is that we can define another (fully observable) random variable, 1, X; > 0, Y₁ = 0, X = 0. Recall Example 5.5 (section 5.3). Use the likelihood ratio to find a 95% confidence interval for theta based on data in Table 5.1 ~ Then, Y; Binomial(1, pi), where = Pi P(Y - 1) = P(X; > 0) = 1 - P(X = 0) = e -Ovi (Ovi)º = 1. = 1 − e−vi 0!
Transcribed Image Text:Example 5.5. Recall Example 5.2 (section 5.1.2). Now, suppose that the Xis will not be directly observable. Instead, we will only be able to observe whether X>0 or X = 0. For example, drivers may not want to reveal to an insurance company that they've had a number of accidents in the past for this will surely increase their premium, but, to mitigate the risk of the insurance industry, government reg- ulations may require that they have to reveal something. So a compromise is reached to balance privacy and transparency-drivers must reveal whether they've had any accident at all (i.e. whether X; > 0 or X; = 0), although they need not reveal exactly how many they've had. Perhaps somewhat surprisingly, we can still estimate the parameter 0 in this case, despite the added complication! The key insight here is that we can define another (fully observable) random variable, 1, X; > 0, Y₁ = 0, X = 0. Recall Example 5.5 (section 5.3). Use the likelihood ratio to find a 95% confidence interval for theta based on data in Table 5.1 ~ Then, Y; Binomial(1, pi), where = Pi P(Y - 1) = P(X; > 0) = 1 - P(X = 0) = e -Ovi (Ovi)º = 1. = 1 − e−vi 0!
Table 5.1 Number of individuals (out of 40) who had zero (X; = 0) or at least one (X; > 0) incident, along with their level of activity (v;) One + Vi (X; > 0) Zero (X = 0) Text 8 10 Text 0 4 2 1 873 2 Recall Example 5.5 (section 5.3). Use the likelihood ratio to find 3 7 a 95% confidence interval for theta based on data in Table 5.1 Source: authors.
Transcribed Image Text:Table 5.1 Number of individuals (out of 40) who had zero (X; = 0) or at least one (X; > 0) incident, along with their level of activity (v;) One + Vi (X; > 0) Zero (X = 0) Text 8 10 Text 0 4 2 1 873 2 Recall Example 5.5 (section 5.3). Use the likelihood ratio to find 3 7 a 95% confidence interval for theta based on data in Table 5.1 Source: authors.
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