Derive mles of probabilities a b and c and determine the

Question

Topic: Advanced Statistics-Categorical Data Analysis

Problem - 3 x 3 joint distribution table is given below. Consider testing the following type of symmetry in the table:

A	B	A
B	C	B
A	B	A

Cells marked A have equal probability, and cells marked B also have equal probability. If the observed counts are y₁₁, y₁₂, y₁₃, y₂₁, y₂₂, y₂₃, y₃₁, y₃₂, y₃₃, derive MLE?s of probabilities A, B, and C, and determine the number of degrees of freedom for the LR goodness-of fit statistic.

Need detailed answers for each question, which includes results, explanation and conclusion step by step.