Answer Happy

Apostolos, believes there are twice as many OU undergraduate students aged between 25 and 35 years of age, as there are below 25 years of age. He defines a random variable Y, which assigns a numerical value to each of three age categories; under 25 years, 25–35 years and over 35 years of age. He also defines 6 to be the probability that a student is less than 25 years old. Using these definitions he created the following table which represents the p.m.f. for the random variable Y. Age 35 Y 1 2 3 Probability 0 20 (1-30) (a) Explain why @ must be less than :
(b) Apostolos uses the ages of 544 students who started to study M248 in October 2020 to produce the following table. Outcome 1 2 3 Frequency 83 197 264 Show that the likelihood of A based on this data is L(O) = C0280 (1 - 30)264, where C is a positive constant not dependent on 0.
Produce a sketch, by hand, of the likelihood function given in part (b), carefully labelling your axes and the maximum likelihood estimate.