1. Who is the king of late night TV? An Internet survey estimates that, when given a choice between David Letterman and Jay Leno, 52% of the population prefers to watch Jay Leno. Three late night TV watchers are randomly selected and asked which of the two talk show hosts they prefer.
a Find the probability distribution for Y , the number of viewers in the sample who prefer Leno.
b Construct a probability histogram for p(y).
c What is the probability that exactly one of the three viewers prefers Leno?
d What are the mean and standard deviation for Y ?
e What is the probability that the number of viewers favoring Leno falls within 2 standard deviations of the mean?
2. A single cell can either die, with probability .1, or split into two cells, with probability .9, producing a new generation of cells. Each cell in the new generation dies or splits into two cells independently with the same probabilities as the initial cell. Find the probability distribution for the number of cells in the next generation.