Consider writing onto a computer disk and then sending it through a certifier that counts the number of missing pulses. Suppose this number x has a Poisson distribution with parameter μ = 0.5. (Round your answers to three decimal places.) (a) What is the probability that a disk has exactly one missing pulse?
(b) What is the probability that a disk has at least two missing pulses?
(c) lf two disks are independently selected, what is the probability that neither contains a missing pulse?

Explained below.

Step-by-step explanation:

The random variable X is defined as the number of missing pulses and follows a Poisson distribution with parameter (μ = 0.50).

The probability mass function of X is as follows:

(a)

Compute the probability that a disk has exactly one missing pulse as follows:

Thus, the probability that a disk has exactly one missing pulse is 0.3033.

(b)

Compute the probability that a disk has at least two missing pulses as follows:

Thus, the probability that a disk has at least two missing pulses is 0.0902.

(c)

It is provided that the two disks selected are independent of each other.

The probability that a disk has no missing pulses is:

Compute the probability that neither of the two disks contains a missing pulse as follows:

Thus, the probability that neither of the two disks contains a missing pulse is 0.3678.

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