Question

9.89 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?

Answer 1

Solution - from the information, observe that the probability p of tossing heads on an unbiased coin is either The coin is tossed tossed twice twice and and for a value a y, the number of heads, is observed. Consider, Y., Y, – – – –, Yn be the random sample from poisson distribution with meal x 2(x) = 2(71, 12,. –––, In (d) = T & (xi) Yi -n na iz Y! function Apply logarithm to the above log ( 2 (x)} = log / er Dog (en") + logo = -2x = log (tl) – log (17 %)

=anx + 2 yi log (1) - log (Thri) Apply equate differentiation with it to zelo respect to x and dlog (e (1) - - A - PAC đao ( 1 ) - i Ms a ý is the estimator likelihood required maximum of do