Exercise 14. Let X₁, X2, X3 be independent Bernoulli trials, i.e. the X, are i.i.d. random variables with P(X₂ = 1) = p and P(X₂ = 0) = 1-p. We want to make inference about p, from observations 1, 2, 3 € {0, 1}. Assume we already know that either p = 0.3 or p = 0.8, and other values of p are not possible. In this case we want to decide whether the hypothesis Ho: p = 0.3 or the alternative H₁: p = 0.8 is more likely. Consider the test which rejects Ho if and only if s = => 2. For this test, determine the probabilities of type I and type II errors. 3
Exercise 14. Let X₁, X2, X3 be independent Bernoulli trials, i.e. the X, are i.i.d. random variables with P(X₂ = 1) = p and P(X₂ = 0) = 1-p. We want to make inference about p, from observations 1, 2, 3 € {0, 1}. Assume we already know that either p = 0.3 or p = 0.8, and other values of p are not possible. In this case we want to decide whether the hypothesis Ho: p = 0.3 or the alternative H₁: p = 0.8 is more likely. Consider the test which rejects Ho if and only if s = => 2. For this test, determine the probabilities of type I and type II errors. 3
MATLAB: An Introduction with Applications
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![Exercise 14. Let X₁, X2, X3 be independent Bernoulli trials, i.e. the X; are i.i.d. random variables
with P(X₂ = 1) = p and P(X; = 0) = 1-p. We want to make inference about p, from observations
x1, x2, x3 = {0, 1}.
-
Assume we already know that either p = 0.3 or p = 0.8, and other values of p are not possible.
In this case we want to decide whether the hypothesis Ho: p = 0.3 or the alternative H₁: p = 0.8
is more likely. Consider the test which rejects Ho if and only if s := ³-₁ ; ≥ 2. For this test,
determine the probabilities of type I and type II errors.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea7bbfe4-f0d9-4343-839c-f9e5c129de8e%2F6ee50d15-fe2b-4925-98a9-a83e033f9623%2Fzpwjd3a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercise 14. Let X₁, X2, X3 be independent Bernoulli trials, i.e. the X; are i.i.d. random variables
with P(X₂ = 1) = p and P(X; = 0) = 1-p. We want to make inference about p, from observations
x1, x2, x3 = {0, 1}.
-
Assume we already know that either p = 0.3 or p = 0.8, and other values of p are not possible.
In this case we want to decide whether the hypothesis Ho: p = 0.3 or the alternative H₁: p = 0.8
is more likely. Consider the test which rejects Ho if and only if s := ³-₁ ; ≥ 2. For this test,
determine the probabilities of type I and type II errors.
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