a) What is the probability that a disk has exacly one missing pulse?

b) What is the probability that a disk has at least two missing pulses?

c) If two disks are independently selected, what is the probability that neither contains a missing pulse?

Owen Mathis
2022-11-03
Answered

Consider writing a computer disk and then sending it throught a certifier that counts the number of missing pulses. Suppose this number X has a Poisson distribution with parameter $\mu =0.3$

a) What is the probability that a disk has exacly one missing pulse?

b) What is the probability that a disk has at least two missing pulses?

c) If two disks are independently selected, what is the probability that neither contains a missing pulse?

a) What is the probability that a disk has exacly one missing pulse?

b) What is the probability that a disk has at least two missing pulses?

c) If two disks are independently selected, what is the probability that neither contains a missing pulse?

You can still ask an expert for help

Savanna Smith

Answered 2022-11-04
Author has **17** answers

pmf of P.D is $=f(k)=e-\lambda \frac{\lambda x}{x}$!where$\lambda $ = parameter of the distribution. x = is the number of independent trials

I.

mean = $\lambda $

= 0.3

A.

$P(X=1)={e}^{-0.3}\cdot {0.3}^{1/1!}=0.22225$

B.

$P(X<2)=P(X=1)+P(X=0)={e}^{-0.3}\cdot {1}^{1/1!}+{e}^{-0.3}{\cdot}^{0/0!}=0.96306,$

$P(X>=2)=1-P(X<2)=0.03694$

C.

the probability of choosing a missing pulse ,

$P(X=0)={e}^{-0.3}\cdot {0.3}^{0/0!}=0.74082$

now, 2 disks are independently selected

$X\sim B(2,0.4082)$

$P(X=0)=(20)\cdot ({0.74082}^{0})\cdot (1-0.74082{)}^{2}$

$=0.0672$

I.

mean = $\lambda $

= 0.3

A.

$P(X=1)={e}^{-0.3}\cdot {0.3}^{1/1!}=0.22225$

B.

$P(X<2)=P(X=1)+P(X=0)={e}^{-0.3}\cdot {1}^{1/1!}+{e}^{-0.3}{\cdot}^{0/0!}=0.96306,$

$P(X>=2)=1-P(X<2)=0.03694$

C.

the probability of choosing a missing pulse ,

$P(X=0)={e}^{-0.3}\cdot {0.3}^{0/0!}=0.74082$

now, 2 disks are independently selected

$X\sim B(2,0.4082)$

$P(X=0)=(20)\cdot ({0.74082}^{0})\cdot (1-0.74082{)}^{2}$

$=0.0672$

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