You have a device that wants to transmit many packets to a router, which is some

Question

You have a device that wants to transmit many packets to a router, which is sometimes busy serving other users. At every second, your device attempts to send a packet. It succeeds with probability 1/5 and the attempts are independent of one another.

a)What is the probability that the first packet gets through in 3 or fewer attempts? (Please enter your answer up to the first three significant decimal places.)

You have a device that wants to transmit many packets to a router, which is sometimes busy serving other users. At every second, your device attempts to send a packet. It succeeds with probability 1/5 and the attempts are independent of one another.

a)What is the probability that the first packet gets through in 3 or fewer attempts? (Please enter your answer up to the first three significant decimal places.)

Explanation / Answer

Ans:

Given that

probability of success,p=1/5=0.2

a)use geometric distribution)

P(x<=3)=0.2+0.8*0.2+0.8^2*0.2=0.488

b)Use binomial distribution with n=20 and p=0.2

P(x>=5)=1-P(x<=4)=1-binomcdf(20,0.2,4)=0.370

c)Use binomial distribution with n=20 and p=0.2

P(x>=5)=1-P(x<=4)=1-binomcdf(20,0.2,4)=0.370

d)Use geometric distribution:

Average number of attempts=1/0.2=5

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