A new battery’s voltage may be acceptable (A) orunaccept- able (U). A certain flashlight requires twobatteries, so bat- teries will be independently selected and testeduntil two acceptable ones have been found. Suppose that 90% of allbatteries have acceptable voltages. Let Y denote thenumber of batteries that must be tested.
a) What is p(2), that is, P(Y 52)?
b) What is p(3)? [Hint: There are twodifferent outcomes
that result in Y 5 3.]
c) To have Y 5 5, what must be true of the fifthbattery
selected? List the four outcomes for which Y 5 5and
then determine p(5).
d) Use the pattern in your answers for parts (a)–(c) toobtain
a general formula for p(y)
e) instead of the random variable Y given in the textbook,define a Negative Binomial random variable and do this question.Also, state the mean and standard deviation for this negativebinomial random variable and interpret it in the context of thequestion
