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given probability mass function:

x 1 2 3 4

p(x) 1/4(θ+2) 1/4(θ) 1/4(1-θ) 1/4(1-θ)

Marbles

1=green

2=blue

3=red

4=white

For 3839 randomly picked marbles

green=1997

blue=32

red=906

white=904

what is the max likelihood of θ using this data?

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# Maximum likelihood estimate

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