Question

In: Statistics and Probability

If you conduct and experiment 1500 times independently, i=1,2,3,...1500. Let y1, y2.... yN be i.i.d observations...

  1. If you conduct and experiment 1500 times independently, i=1,2,3,...1500. Let y1, y2.... yN be i.i.d observations from this experiment, yi=1 if heads with a probability of β; yi=0 if tails with a probability of 1-β. If you get 600 heads and 900 tails, what is the βMLE
A.

0.4

B.

0.5

C.

0.6

D.

0.7

Solutions

Expert Solution

The random variable is given by:

Or, in other terms,


The likelihood function is given by:




Now the MLE of is given by the for which,






Here, it is given that,



Hence,


Hence, option a) is correct.

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