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Two binary channels have been connected in a cascade as shown in the figure.
It is given that P(x1) = 0.7 and P(x2) = 0.3, then choose correct option from below.
It is given that P(x1) = 0.7 and P(x2) = 0.3, then choose correct option from below.
- a)P(z1) =0.547
- b)P(z2) =0.453
- c)P(x2/y1) =0.376
- d)P(x2/y1) =0.176
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Two binary channels have been connected in a cascade as shown in the f...
For a binary channel as shown below
P(yn) = P(xm)P(yn/xm) , n = 1,2 and m = 1,2
Where,
P(yn) → Probability of receiving output yn
P(xm) → Probability of the transmitting signal
P(yn/xm) → Probability of the received output provided x was transmitted
P(xm/yn) = [P(yn/xm)× P(xm)]/P(yn)
Where;
P(xm/yn) → Probability of xm transmitted given that yn was received
Calculation of P(z1);
The marked line shows the path from x1 to z1 (abc and aec) and x2 to z1 (dec and dbc)
Following these paths, we can calculate P(z1)
P(z1) = [P(x1) {(0.6× 0.4) or(0.4 × 0.7}] or [P(x2){(0.3 × 0.4) or (0.7 × 0.7)}]
⇒ P(z1) = [0.7 {(0.6× 0.4) + (0.4 × 0.7}] + [0.3{(0.3 × 0.4) + (0.7 × 0.7)}]
∴ P(z1) = 0.547
Similarly, P(z2) can be calculated;
P(z2) = [P(x1) {(0.6× 0.6) +(0.4 × 0.3}] + [P(x2){(0.3 × 0.6) + (0.7 × 0.3)}] = 0.453
Calculation of P(x2/y1):
P(y1) = (0.7 × 0.6) + (0.3 × 0.3) = 0.51
P(yn) = P(xm)P(yn/xm) , n = 1,2 and m = 1,2
Where,
P(yn) → Probability of receiving output yn
P(xm) → Probability of the transmitting signal
P(yn/xm) → Probability of the received output provided x was transmitted
P(xm/yn) = [P(yn/xm)× P(xm)]/P(yn)
Where;
P(xm/yn) → Probability of xm transmitted given that yn was received
Calculation of P(z1);
The marked line shows the path from x1 to z1 (abc and aec) and x2 to z1 (dec and dbc)
Following these paths, we can calculate P(z1)
P(z1) = [P(x1) {(0.6× 0.4) or(0.4 × 0.7}] or [P(x2){(0.3 × 0.4) or (0.7 × 0.7)}]
⇒ P(z1) = [0.7 {(0.6× 0.4) + (0.4 × 0.7}] + [0.3{(0.3 × 0.4) + (0.7 × 0.7)}]
∴ P(z1) = 0.547
Similarly, P(z2) can be calculated;
P(z2) = [P(x1) {(0.6× 0.6) +(0.4 × 0.3}] + [P(x2){(0.3 × 0.6) + (0.7 × 0.3)}] = 0.453
Calculation of P(x2/y1):
P(y1) = (0.7 × 0.6) + (0.3 × 0.3) = 0.51
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Two binary channels have been connected in a cascade as shown in the figure.It is given that P(x1) = 0.7 and P(x2) = 0.3, then choose correct option from below.a)P(z1) =0.547b)P(z2) =0.453c)P(x2/y1) =0.376d)P(x2/y1) =0.176Correct answer is option 'D'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2025 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Two binary channels have been connected in a cascade as shown in the figure.It is given that P(x1) = 0.7 and P(x2) = 0.3, then choose correct option from below.a)P(z1) =0.547b)P(z2) =0.453c)P(x2/y1) =0.376d)P(x2/y1) =0.176Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two binary channels have been connected in a cascade as shown in the figure.It is given that P(x1) = 0.7 and P(x2) = 0.3, then choose correct option from below.a)P(z1) =0.547b)P(z2) =0.453c)P(x2/y1) =0.376d)P(x2/y1) =0.176Correct answer is option 'D'. Can you explain this answer?.
Two binary channels have been connected in a cascade as shown in the figure.It is given that P(x1) = 0.7 and P(x2) = 0.3, then choose correct option from below.a)P(z1) =0.547b)P(z2) =0.453c)P(x2/y1) =0.376d)P(x2/y1) =0.176Correct answer is option 'D'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2025 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Two binary channels have been connected in a cascade as shown in the figure.It is given that P(x1) = 0.7 and P(x2) = 0.3, then choose correct option from below.a)P(z1) =0.547b)P(z2) =0.453c)P(x2/y1) =0.376d)P(x2/y1) =0.176Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two binary channels have been connected in a cascade as shown in the figure.It is given that P(x1) = 0.7 and P(x2) = 0.3, then choose correct option from below.a)P(z1) =0.547b)P(z2) =0.453c)P(x2/y1) =0.376d)P(x2/y1) =0.176Correct answer is option 'D'. Can you explain this answer?.
Solutions for Two binary channels have been connected in a cascade as shown in the figure.It is given that P(x1) = 0.7 and P(x2) = 0.3, then choose correct option from below.a)P(z1) =0.547b)P(z2) =0.453c)P(x2/y1) =0.376d)P(x2/y1) =0.176Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electronics and Communication Engineering (ECE).
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Two binary channels have been connected in a cascade as shown in the figure.It is given that P(x1) = 0.7 and P(x2) = 0.3, then choose correct option from below.a)P(z1) =0.547b)P(z2) =0.453c)P(x2/y1) =0.376d)P(x2/y1) =0.176Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Two binary channels have been connected in a cascade as shown in the figure.It is given that P(x1) = 0.7 and P(x2) = 0.3, then choose correct option from below.a)P(z1) =0.547b)P(z2) =0.453c)P(x2/y1) =0.376d)P(x2/y1) =0.176Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Two binary channels have been connected in a cascade as shown in the figure.It is given that P(x1) = 0.7 and P(x2) = 0.3, then choose correct option from below.a)P(z1) =0.547b)P(z2) =0.453c)P(x2/y1) =0.376d)P(x2/y1) =0.176Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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