Ch 14 "observing a single value of x" and "given x"

[Molly]

Hi all,

i understand when the question states "observing a single value of x" we do not need to do the product of the likelihood function. But in question 4 it doesnt specify that we only have one value of x, and it says "yields x successes", so i would have thought that we would be thinking of more than one value of x here. However the answers should the likelihood function to be
p^x (1-p)^(n-x) where as i would have thought it would be p^\sumx_i (1-p)^(n-\sumx_i)

Is there a reason for this? is there an easy way i can tell when we need to find the product and when we dont?

Thanks

 

[CapitalActuary]

I have no idea what you’re referring to as I don’t have any of the notes, but it sounds like perhaps x in the course notes is referring to the sum of b_i where b_i is 1 if a success or 0 otherwise. i.e. each b term is an observation of an individual success or failure, but the x is the observation of the total number of successes.

Whereas you are using each x_i like I am using b_i above.

Sounds to me like a difference in notation, without knowing more.

 

[Molly]

I have no idea what you’re referring to as I don’t have any of the notes, but it sounds like perhaps x in the course notes is referring to the sum of b_i where b_i is 1 if a success or 0 otherwise. i.e. each b term is an observation of an individual success or failure, but the x is the observation of the total number of successes.

Whereas you are using each x_i like I am using b_i above.

Sounds to me like a difference in notation, without knowing more.

ah that does make sense thank you, so definitely something to look out for when using the binomial distributions!