# Could someone verify my logic for managing probability distributions in an experiment

#### tkessler

##### New Member
I'm not well versed in stats lingo, but am hoping my logic in the concepts here makes sense and is correct.

Often in my work (measuring electrical responses of cells) I take of more than one independent measure per sample, such as the time to an event occurring, along with the size of that event, and the decay time of that event.

In this sense, per sample (per cell) I may have three (or more) distinct random measurements:

Time to Event (T)
Size of Event (S)
Decay time (D)

For a given sample, each of these measures are continuous and will therefore have a separate probability density function, such as f(T), f(S), and f(D), among others that may or may not be included.

For these measures, I'm mainly curious if we can set up a linear combination to represent the given measures as a single one on a per-sample basis:

Y=T+S+D

This seems quite doable, as it will give a single measure "Y" that combines those of interest, and from which we can get a single expectation of these measures:

E(Y)=E(T)+E(S)+E(D)

...and then continue for other computations like variance, etc., for this one sample.

Is this approach standard for computations on this kind of data, or is it taking a more complicated route?

My concern here has been the handling of multiple measures per sample, but if my understanding is correct, with the management of them in a linear combination as with Y above, I'd expect we could multiply the set of measures by a coefficient vector that cancels out unwanted measures (or adjusts them linearly), and then continue to calculate expectation, variance, etc., to describe or infer from the remaining data.

To that extent, and for what it's worth, this approach would sum the measurements into one, similar to the way a simpler experiment is handled, such as a coin toss that only has one count/measure per experiment.

From here, having the measured samples compacted into one would then allow me to computer population statistics on multiple such samples, such as the following for many cell measurements (denoted by Y above):

Q=Y1+Y2+...+Yn

The vector Q could then be subject to averaging, additional expectation measures, and other details to outline the population description.

Its been a long time for me to get this as an understanding...I'm hoping its correct. If anyone has feedback, I'd love to hear it. 