Design a lr test to choose between the, Electrical Engineering

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Design a lr test to choose between the

1. a. Design a LR test to choose between the hypotheses:
H1 : The sample X is chi-squared distributed with n = 6 degrees of freedom.
H0 : The sample X is chi-squared distributed with 2 degrees of freedom.
Assume equal prior probabilities and equal costs of error.
b. Suppose the number of degrees of freedom in H1 is a discrete random variable such that
P(n = N = 6) = 1/2 and P(n = M = 8) = 1/2. What is the LR test for this case?

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