MLE problem

[Chandrima]

Can anyone help me in understanding this problem? I am not being able to understand which distribution this sum follows. Hence, not sure how to write the likelihood function. Please help. (ref. to the two files attached herewith)

 

[Aditya mohan mathur]

In cases like this, when the frequency and the probabilities of different events are given, we obtain the likelihood function by, say,
L= P1^f1 ×P2^f2 and so on for all the events.
Here it will be 'probability of going up' to the power it's 'frequency' multiplied similarly with both other events function

 

[Chandrima]

Thank you Aditya for your help. Now I could do (ii), (iii)(a) and (iii)(b). But I am stuck at solving the easiest part i.e. (i). For solving (i), I am just solving following three inequalities considering the fact that probability should be between 0 to 1:
0 <= (1/4 - theta) <= 1
0 <= (5/8 + 2*theta) <= 1
0 <= (1/8 - theta) <=1
This is giving rise to (-7/8) <= theta <= (3/16)
But the given answer is (-5/6) <= theta <= (1/8)
Where am I making mistake???

 

[Bharti Singla]

Thank you Aditya for your help. Now I could do (ii), (iii)(a) and (iii)(b). But I am stuck at solving the easiest part i.e. (i). For solving (i), I am just solving following three inequalities considering the fact that
probability should be between 0 to 1:
0 <= (1/4 - theta) <= 1
0 <= (5/8 + 2*theta) <= 1
0 <= (1/8 - theta) <=1
This is giving rise to (-7/8) <= theta <= (3/16)
But the given answer is (-5/6) <= theta <= (1/8)
Where am I making mistake???

Hope this helps!

 

[Chandrima]

Many many thanks Bharti! I really appreciate your prompt help and fast reply. Thank you a lot.

 

[Bharti Singla]

Many many thanks Bharti! I really appreciate your prompt help and fast reply. Thank you a lot.

Your welcome