Staining is frequently used in biology and medicine to put in evidence of structures in tissues for microscopic visualization. Consider a Experience involving the staining of 6 cells. Let X be the number of cells that are correctly colored among n = 6 cells. Suppose X has the probability distribution Following:

x 0 1 2 3 4 5 6

f(x) c/18 c/18 2c/9 c/6 c/3 c/3 c/6

(a) Determine the value of c. (b) Calculate the expected number of cells that are correctly colored. (c) Calculate the following probabilities: (i) P(| X 2| 1); (ii) P(X > +), where and are the mean and standard deviation respectively. the number of cells that are correctly colored.