3. Dr. Tamer helps researches analyze data that come from a flow cytometer A How cytote allows for individual measuremen

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3 Dr Tamer Helps Researches Analyze Data That Come From A Flow Cytometer A How Cytote Allows For Individual Measuremen 1 (28.84 KiB) Viewed 30 times

3. Dr. Tamer helps researches analyze data that come from a flow cytometer A How cytote allows for individual measurements to be taken on cach cell of a sample of blood. Researchers can this to identify what percentage of the sample has a certain type of cell that has a particular function like B-cell, T-cells, etc. The graph below is an example of a flow cytometry data collected from 1000 patients Figure 1: Synthetic Flow Data Set Since the observations are proportions, the values can not be less than or higher than L. we were to see the proportions are a continuando variable, a common distribution that could be wed to model random behavior such as this is the beta distribution. The dentyfuction for the Beta distribution is (*) 1+5)*(1-7)+ 0<x<! г(о)Гta) (a) Use the force a density strategy to show that EXX). Note that the Var(x) (e can be done in a similar way but you do not have to show this for this problem. Hint: Use the property of sama functions discussed in lecture () = (t-1-1). (6) What is the density function of Y - 1 - XP How does this transformation relate back to the distribution of X? It may be helpful to graph an example of the two demities X and Y to gain tight ...perhapeal and 2 (e) Suppose the sample mean and variance of the data provided in Figure 1 ae.I and 008182 espectively te these numbers to determine an appropriate Beta distribution to model the T-cell proportions (round your estimates to the rest intepe). Compute the probability that patients Teell proportion above