Independent production lines each make tennis balls

Reference no: EM13167130

Two independent production lines each make tennis balls in a Poisson manner. One line makes white tennis balls at an average rate of λw balls per hour. The other production line makes yellow tennis balls at an average rate of λy balls per hour. Tennis balls are put into cans as soon as they are produced. Different types of cans are used for white and for yellow balls; colors are never mixed. Each can holds two tennis balls.
a) What is the distribution (PMF) of the number of full cans of white balls produced over one hour?

b) What is the probability that the first can of tennis balls to be filled will be a can of white balls?

c) Find the probability that among the first 10 produced balls, at least 8 will be yellow.

d) If we arrive at a random instant, what is the expectation of T, the time between the moment when the last ball was produced and the moment when the next ball will be produced (independently of color)?

Reference no: EM13167130

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