"One way to separate a mixture of stem cells and differentiated cells is to label the cell population with a specific antibody. Let's say stem cells express exactly 100 copies of the membrane antigen X, while all differentiated cells express exactly 10 copies of X.
To the cell mixture, you add a very large solution of 0.1μM antibody (for X). The Kd (dissociation constant) for the antibody-antigen binding reaction is 1μM (treat antibody as if it has only one binding site).
1) On average, how many antibody molecules will be bound per stem cell? What about per differentiated cell?
2) Find the standard deviation of the of the number of antibodies bound per stem cell (assume binomial distribution)