# maximum likelihood

#### bizan

##### New Member
Hello! I would like to know if what I need to do is feasible.

Given a sample x=[-1 0 2 3], I would like to know the probability (the likelihood) that the sample has been generated by a normal distribution N(2,2).

Thanks a lot, Luis.

#### Dason

What is giving you trouble with this exactly?

#### noetsi

##### No cake for spunky
I never knew that ML told you the probability that a given set of data resulted from a normal distribution.... Its commonly an assumption of the use of ML to generate parameters, but ML does not show you that the distribution is normal. You have to use other test.

Before Dason tells me I am wrong, I note that this is not true (the need for normality) in all use of ML. It is for example commonly in its use in SEM. #### bizan

##### New Member
I see, thank you for the answers.

The problem I have is that some signals are generated from 2 distributions, one N(0,2) and the other N(2,2). I would like a measure of the probability
that the sample generated from N(0,2) could be mismatched with the one coming from N(2,2).

I am thinking of using the p-value of the Kolmogorov-Smirnov test for 2 samples.

#### Dason

I see, thank you for the answers.

The problem I have is that some signals are generated from 2 distributions, one N(0,2) and the other N(2,2). I would like a measure of the probability
that the sample generated from N(0,2) could be mismatched with the one coming from N(2,2).

I am thinking of using the p-value of the Kolmogorov-Smirnov test for 2 samples.
Can you explain what you're trying to do a little more? This post wasn't entirely clear to me. Maybe provide some example data and what you want to be able to do? Thanks.

#### bizan

##### New Member
Yes, let's say there exist 100 students. 50 work hard, and get a signal from a normal distribution N(h,2), h=(0,10). The other 50 shirk and get a signal from a normal distribution N(0,2). That is, if you work hard the signal is higher (for later use).

I am modifying the parameter h, to go from 0 to a very high number. When h is very high anyone who sees the signal can tell for sure the student work hard.
I could use as a measure of how easy is to tell that a student worked hard by using the difference in mean. But I would like something between 0 and 1.

#### Miner

##### TS Contributor
Are you trying to determine the area of overlap of the two distributions? If so, you might consider the probabilistic reliability approach used in to calculate the probability of failure when the distribution of material strength overlaps the distribution of physical stress.

#### bizan

##### New Member
That is a very good idea! Thank you very much, I will study how to apply it.