Given: Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets. To find: Probability (p) that the node “A” succeeds for the first time in slot number 5. Solution: The probability (p) that the node “A” succeeds for the first time in slot number 5 is (1-p(A)) 4 p(A) --- (1) . Here, p (A) is the probability that the node “A” succeeds in any slot. That is: p (A transmits, B, C, and D does not transmit). p(A)=p ( A transmit ) * p ( B does not transmit ) * p ( C does not transmit ) * p(D does not transmit)

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Answer 1

Expert Solution & Answer

Chapter 6, Problem P11P

a.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that the node “A” succeeds for the first time in slot number 5.

Solution:

The probability (p) that the node “A” succeeds for the first time in slot number 5 is (1-p(A))4p(A) --- (1).

Here,

p (A) is the probability that the node “A” succeeds in any slot. That is: p (A transmits, B, C, and D does not transmit).

p(A)=p(A transmit) * p(B does not transmit) * p(C does not transmit) * p(D does not transmit)

b.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that any of the nodes “A”, “B”, “C”, or “D” succeeds in slot number 4.

Solution:

From (a), it is clear that if any node succeeds in any slot, the probability is p(node)=p(1-p)3.

So,

The probability that the node “A” succeeds in slot number 4 is: p(A)=p(1-p)3

The probability that the node “B” succeeds in slot number 4

c.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that 1^st success occurs on slot number 3.

Solution:

Probability of some node occurs in a slot = 4p(1-p)3

Probability of no node succeeds in a slot = 1-4p(1-p)3

Probability of the first success occurs in slot number 3 is determined by multiplying the probability of some node succeeds in a slot and probability of no node succeeds in a slot.

Let p(S) = probability of the 1^st success occurs in slot number 3

d.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Efficiency of the four node system.

Solution:

The efficiency of the four node system is determined by the success of any nodes succeeds in a slot...

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Problem 5: The following shows the schematic of a SCARA robot and its DH parameters. Complete the following questions based on this information. 20 01 21 02. 22 done by ai α; di Ꮎ ; 21 d3 1 a1 0 0 0₁** 2 a2 180° 0 0% 3 0 0 d3 0 The Jacobian matrix of this robot is given below: -a1S1a2S12 -a2S12 J(q) = a1c1 + a2c12 0 a2C12 0 10° (a) For a₁ = 1, a2 = 2, is q = 180° a singularity configuration of this robot? a1 3 [10°1 (b) For a₁ = 1, a2 = 2, is q = | 0° a singularity configuration of this robot? 3

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Answer 2

Expert Solution & Answer

Chapter 6, Problem P11P

a.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that the node “A” succeeds for the first time in slot number 5.

Solution:

The probability (p) that the node “A” succeeds for the first time in slot number 5 is (1-p(A))4p(A) --- (1).

Here,

p (A) is the probability that the node “A” succeeds in any slot. That is: p (A transmits, B, C, and D does not transmit).

p(A)=p(A transmit) * p(B does not transmit) * p(C does not transmit) * p(D does not transmit)

b.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that any of the nodes “A”, “B”, “C”, or “D” succeeds in slot number 4.

Solution:

From (a), it is clear that if any node succeeds in any slot, the probability is p(node)=p(1-p)3.

So,

The probability that the node “A” succeeds in slot number 4 is: p(A)=p(1-p)3

The probability that the node “B” succeeds in slot number 4

c.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that 1^st success occurs on slot number 3.

Solution:

Probability of some node occurs in a slot = 4p(1-p)3

Probability of no node succeeds in a slot = 1-4p(1-p)3

Probability of the first success occurs in slot number 3 is determined by multiplying the probability of some node succeeds in a slot and probability of no node succeeds in a slot.

Let p(S) = probability of the 1^st success occurs in slot number 3

d.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Efficiency of the four node system.

Solution:

The efficiency of the four node system is determined by the success of any nodes succeeds in a slot...

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Expert Solution & Answer

Chapter 6, Problem P11P

a.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that the node “A” succeeds for the first time in slot number 5.

Solution:

The probability (p) that the node “A” succeeds for the first time in slot number 5 is (1-p(A))4p(A) --- (1).

Here,

p (A) is the probability that the node “A” succeeds in any slot. That is: p (A transmits, B, C, and D does not transmit).

p(A)=p(A transmit) * p(B does not transmit) * p(C does not transmit) * p(D does not transmit)

b.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that any of the nodes “A”, “B”, “C”, or “D” succeeds in slot number 4.

Solution:

From (a), it is clear that if any node succeeds in any slot, the probability is p(node)=p(1-p)3.

So,

The probability that the node “A” succeeds in slot number 4 is: p(A)=p(1-p)3

The probability that the node “B” succeeds in slot number 4

c.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that 1^st success occurs on slot number 3.

Solution:

Probability of some node occurs in a slot = 4p(1-p)3

Probability of no node succeeds in a slot = 1-4p(1-p)3

Probability of the first success occurs in slot number 3 is determined by multiplying the probability of some node succeeds in a slot and probability of no node succeeds in a slot.

Let p(S) = probability of the 1^st success occurs in slot number 3

d.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Efficiency of the four node system.

Solution:

The efficiency of the four node system is determined by the success of any nodes succeeds in a slot...

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Expert Solution & Answer

Chapter 6, Problem P11P

a.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that the node “A” succeeds for the first time in slot number 5.

Solution:

The probability (p) that the node “A” succeeds for the first time in slot number 5 is (1-p(A))4p(A) --- (1).

Here,

p (A) is the probability that the node “A” succeeds in any slot. That is: p (A transmits, B, C, and D does not transmit).

p(A)=p(A transmit) * p(B does not transmit) * p(C does not transmit) * p(D does not transmit)

b.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that any of the nodes “A”, “B”, “C”, or “D” succeeds in slot number 4.

Solution:

From (a), it is clear that if any node succeeds in any slot, the probability is p(node)=p(1-p)3.

So,

The probability that the node “A” succeeds in slot number 4 is: p(A)=p(1-p)3

The probability that the node “B” succeeds in slot number 4

c.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that 1^st success occurs on slot number 3.

Solution:

Probability of some node occurs in a slot = 4p(1-p)3

Probability of no node succeeds in a slot = 1-4p(1-p)3

Probability of the first success occurs in slot number 3 is determined by multiplying the probability of some node succeeds in a slot and probability of no node succeeds in a slot.

Let p(S) = probability of the 1^st success occurs in slot number 3

d.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Efficiency of the four node system.

Solution:

The efficiency of the four node system is determined by the success of any nodes succeeds in a slot...

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Expert Solution & Answer

Answer 6

Expert Solution & Answer

Answer 7

Chapter 6, Problem P11P

a.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that the node “A” succeeds for the first time in slot number 5.

Solution:

The probability (p) that the node “A” succeeds for the first time in slot number 5 is (1-p(A))4p(A) --- (1).

Here,

p (A) is the probability that the node “A” succeeds in any slot. That is: p (A transmits, B, C, and D does not transmit).

p(A)=p(A transmit) * p(B does not transmit) * p(C does not transmit) * p(D does not transmit)

b.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that any of the nodes “A”, “B”, “C”, or “D” succeeds in slot number 4.

Solution:

From (a), it is clear that if any node succeeds in any slot, the probability is p(node)=p(1-p)3.

So,

The probability that the node “A” succeeds in slot number 4 is: p(A)=p(1-p)3

The probability that the node “B” succeeds in slot number 4

c.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that 1^st success occurs on slot number 3.

Solution:

Probability of some node occurs in a slot = 4p(1-p)3

Probability of no node succeeds in a slot = 1-4p(1-p)3

Probability of the first success occurs in slot number 3 is determined by multiplying the probability of some node succeeds in a slot and probability of no node succeeds in a slot.

Let p(S) = probability of the 1^st success occurs in slot number 3

d.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Efficiency of the four node system.

Solution:

The efficiency of the four node system is determined by the success of any nodes succeeds in a slot...

Answer 8

Chapter 6, Problem P11P

a.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that the node “A” succeeds for the first time in slot number 5.

Solution:

The probability (p) that the node “A” succeeds for the first time in slot number 5 is (1-p(A))4p(A) --- (1).

Here,

p (A) is the probability that the node “A” succeeds in any slot. That is: p (A transmits, B, C, and D does not transmit).

p(A)=p(A transmit) * p(B does not transmit) * p(C does not transmit) * p(D does not transmit)

Answer 9

Chapter 6, Problem P11P

a.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that the node “A” succeeds for the first time in slot number 5.

Solution:

The probability (p) that the node “A” succeeds for the first time in slot number 5 is (1-p(A))4p(A) --- (1).

Here,

p (A) is the probability that the node “A” succeeds in any slot. That is: p (A transmits, B, C, and D does not transmit).

p(A)=p(A transmit) * p(B does not transmit) * p(C does not transmit) * p(D does not transmit)

Answer 10

b.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that any of the nodes “A”, “B”, “C”, or “D” succeeds in slot number 4.

Solution:

From (a), it is clear that if any node succeeds in any slot, the probability is p(node)=p(1-p)3.

So,

The probability that the node “A” succeeds in slot number 4 is: p(A)=p(1-p)3

The probability that the node “B” succeeds in slot number 4

Answer 11

b.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that any of the nodes “A”, “B”, “C”, or “D” succeeds in slot number 4.

Solution:

From (a), it is clear that if any node succeeds in any slot, the probability is p(node)=p(1-p)3.

So,

The probability that the node “A” succeeds in slot number 4 is: p(A)=p(1-p)3

The probability that the node “B” succeeds in slot number 4

Answer 12

c.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that 1^st success occurs on slot number 3.

Solution:

Probability of some node occurs in a slot = 4p(1-p)3

Probability of no node succeeds in a slot = 1-4p(1-p)3

Probability of the first success occurs in slot number 3 is determined by multiplying the probability of some node succeeds in a slot and probability of no node succeeds in a slot.

Let p(S) = probability of the 1^st success occurs in slot number 3

Answer 13

c.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that 1^st success occurs on slot number 3.

Solution:

Probability of some node occurs in a slot = 4p(1-p)3

Probability of no node succeeds in a slot = 1-4p(1-p)3

Probability of the first success occurs in slot number 3 is determined by multiplying the probability of some node succeeds in a slot and probability of no node succeeds in a slot.

Let p(S) = probability of the 1^st success occurs in slot number 3

Answer 14

d.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Efficiency of the four node system.

Solution:

The efficiency of the four node system is determined by the success of any nodes succeeds in a slot...

Answer 15

d.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Efficiency of the four node system.

Solution:

The efficiency of the four node system is determined by the success of any nodes succeeds in a slot...

Answer 16

Expert Solution & Answer

Answer 17

Expert Solution & Answer

Answer 18

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Answer 19

Ch. 6 - Consider the transportation analogy in Section...Ch. 6 - If all the links in the Internet were to provide...Ch. 6 - Prob. R3RQ Ch. 6 - Prob. R4RQ Ch. 6 - Prob. R5RQ Ch. 6 - Prob. R6RQ Ch. 6 - Prob. R7RQ Ch. 6 - Prob. R8RQ Ch. 6 - Prob. R9RQ Ch. 6 - Prob. R10RQ

Solution Summary: The author explains how to find the probability that the node "A" succeeds in slot number 5 by substituting the value of p (A) in equation (1).

Explanation of Solution

Explanation of Solution

Explanation of Solution

Explanation of Solution

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Chapter 6 Solutions