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It is known that the probability p of tossing heads on an unbalanced coin is either 1/4 or 3/4. The coin is tossed twice and a value for Y , the number of heads, is observed. For each possible value of Y , which of the two values for p (1/4 or 3/4) maximizes the probability that Y = y? Depending on the value of y actually observed, what is the MLE of p?

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On solving the provided question we can say that NILE is not unique for this case

What is Probability?

Probability is the possibility or chance that something will happen. Probability = how many different paths there are to success/the total number of events that might occur. A coin flip, for instance, has a 50% chance of coming up heads since there is only one method to acquire a head and there are a total of two possible outcomes (a head or tail). P(heads) = 1/2 is the formula.

Note: the probability is equal to the mass function for Y :2

since,  ML criteria, we choose p which maximizes the probability.

If Y 0, L (p) is maximized at p 0.25.

If Y 2, L (p) is maximized at p 0.75.

[tex]But if Y 1, L (p) has the same value at both as shown above; that is,[/tex]

L (0.25) L (0.75) for y — 1.

NILE is not unique for this case

To know more about probability  visit:
https://brainly.com/question/11234923

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