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Probability
Review
Given
N = populationX = sample sizeP = probability of success/eventQ = 1-P, probability of failure/non event
Wanted
Probability of X successes in population of N where member event occurs with probability P
Solution
BiCoef(N,X) PXQ(N-X)N!--------------- PXQ(N-X)X! (N-X)!
Example
What is probability of having 4 heads after flipping a coin 6 times?N = 6X = 4P = ½Q = 1 – P6! 30------- (.5)6= ----- 0.0156 = 0.234 or 23.4%4!2! 2
Example
What is probability of having 7 heads after flipping a coin 7 times with atrick coin?N = 6X = 4P = .9Q = 1 – P7!------- (.9)7(.1)0=(.9)7=.4787!0!
Problems
Solver Guide
Similar to Chapter 1 Problem12
A packet switch receives a packet and determines the outbound link to which the packet should be forwarded. When the packet arrives, one other packet is halfway done being transmitted on this outbound link and 480 other packets are waiting to be transmitted. Packets are transmitted in order of arrival.Supposeall packets are 64 bytes and the link is 40Gbps.What is the queuing delay for the packet?
Similar to Chapter 1 Problem12
Whatis the queuing delay for the packet?Queingdelay =((L*(Q+1)– B*L)/(R)= 6.15usec
Similar to Chapter 1 Problem16
Consider a router bufferprecedingan outbound link. In this problem you will use Little'sformula, a famous formula from queuing theory.Let N denote the average number of packets in the buffer plus the packet being transmitted. Let a denote the rate of packets arriving ". " at the link. Letd denote the average total delay (i.e., the queuing delay plus the transmission delay) experienced by a packet.Little'sformula is N = a · d.Supposethat on average, the buffer contains 360 packets (in addition to the packet currently being transmitted) and the average queuing delay is 300msecThe linkstransmissionrate is 60 packets/sec. Using Little's formula,what is the average packet arrival rate, assuming there is no packet loss?
Similar to Chapter 1 Problem16
Little'sformula is N = a · d.UsingLittle's formula, what is the average packet arrival rate, assuming there is no packet loss?T=1/Ra = N/(Q+T)=1137 packets/sec
Similar to Chapter 1 Problem24
Suppose you would like to urgently deliver 4Tbytesof data from Boston to Los Angeles. You have available a 2.4Gbpsdedicated link for data transfer. Would you prefer to transmit the data via this link or instead use FedEx overnight delivery?Explain.
Similar to Chapter 1 Problem24
Suppose you would like to urgently deliver 4Tbytesof data from Boston to Los Angeles. You have available a 2.4Gbpsdedicated link for data transfer. Would you prefer to transmit the data via this link or instead use FedEx overnight delivery? Explain.4E12*8bits / 2.4E9bps3.704hrsto transmit
Similar to Chapter 1 Problem25
Suppose two host, A and B, are separated by 10,000 km and are connected by a direct link of R = 512 kbps. Suppose the propagation speed over the link is 2.5·108meters/sec.a. Calculate the bandwidth delay product, R·dpropb. Consider sending a file of 48Tbitsfrom Host A to Host B. Suppose the file is sent continuously as one large message.What is the maximum number of bits that will be in the link at any given time?c. Provide an interpretation of the bandwidth delay product.d.What is the width (in meters) of a bit in the link?e. Derive a general expression for the width of a bit in terms of the propagation speed, s, the transmission rate, R, and the length of the link m.
Similar to Chapter 1 Problem25
a. Calculate the bandwidth delay product:R*D/S = 20.48kbitsb. Max bits in link: 20.48kbitsc. bandwidth delay product is the (max) number of bits that could be in the linkd. Width of bit:D/(R*D/S)= S/R = 488.281me. Width of bit =S/R
Similar to Chapter 1 Problem26
Suppose two host, A and B, are separated by 10,000 km and are connected by a direct link, R. Suppose the propagation speed over the link is 2.5·108meters/sec.For what value of R is the width of a bit as long as the length of the link?
Similar to Chapter 1 Problem26
Suppose two host, A and B, are separated by 10,000 km and are connected by a direct link, R. Suppose the propagation speed over the link is 2.5·108meters/sec. For what value of R is the width of a bit as long as the length of the link?R= (S /width_of_bit)=S/D = 25bps
Similar to Chapter 1 Problem 28
Suppose two host, A and B, are separated by 100 km and are connected by a direct link of R = 56 kbps and will send a file of 350Gbytes. Suppose the propagation speed over the link is 2.5·108meters/sec.a.How long does it take to send the file, assuming it is sentcontinuously?b. Suppose not the file is broken into packets of length 1.45kbits. Suppose that each packet is acknowledged by the receiver and the transmission time of the acknowledgment is negligible. Finally assume that the sender cannot send a packet until the preceding one is acknowledged.How long does it take to send the file?c.Comparethe results from (a) and (b).
Similar to Chapter 1 Problem 28
a. Howlong does it take to send the file, assuming it is sent continuously?Transmission delay + Propagation Delay=F/R+D/S=350E9bytes / 56kbps +100km/2.5E8mps=19.29 monthsb. Supposenowthe file is broken into packets of length 1.45kbits. Suppose that each packet is acknowledged by the receiver and the transmission time of the acknowledgment is negligible. Finally assume that the sender cannot send a packet until the preceding one is acknowledged. How long does it take to send the file?NumPackets*2*Prop delay + Transmission delay(F/P)*2D/S+ F/R= 19.29months + 25.7 minc. Compare the results from (a) and (b).
Similar to Chapter 1 Problem 29
Suppose there is a 10 Mbps microwave link between a geostationary satellite and its base station on Earth. Every minute the satellite takes a digital photo and sends it to the base station. Assume a propagation speed of 2.4·108meters/sec.a.Whatis the propagation delay of the link?b. What is thebandwidth delay product,R·dprop?c. Let x denote the size of the photo.What is the minimum value of x for the microwave link to be continuously transmitting?
Similar to Chapter 1 Problem 29
a. Whatis the propagation delay of the link?D/S=150msecb. What is the bandwidth delay product,R·dprop?R*D/S=1.5Mbitsc. Let x denote the size of the photo. What is the minimum value of x for the microwave link to be continuously transmitting?1min*R =600Mbitsor 75 Mbytes

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Problems - uwa.dyessick.com