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A random variable X takes -1 and +1 with probabilities 0.2 and 0.8, respectively. It is transmitted across a channel which adds noise N, so that the random variable at the channel output is Y = X + N. The noise n is independent of X, and is uniformly distributed over the interval [-2, 2]. The receiver makes a decision
Where the threshold θ ∈ [-1, 1] is chosen so as to minimize the probability of error Pr The minimum probability of error, rounded off to 1 decimal place, is ______________.
    Correct answer is '0.1'. Can you explain this answer?
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    A random variable X takes -1 and +1 with probabilities 0.2 and 0.8, re...
    =0.05 – 0.5Vth + 0.2Vth + 0.2
    Pe = 0.25 + 0.15Vth
    For Vth = 0 → Pe = 0.25
    For Vth = 1 → Pe = 0.4
    For Vth = –1 → Pe = 0.1
    ∴ Minimum probability of error = 0.1
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    A random variable X takes -1 and +1 with probabilities 0.2 and 0.8, respectively. It is transmitted across a channel which adds noise N, so that the random variable at the channel output is Y = X + N. The noise n is independent of X, and is uniformly distributed over the interval [-2, 2]. The receiver makes a decisionWhere the threshold θ ∈ [-1, 1] is chosen so as to minimize the probability of error Pr The minimum probability of error, rounded off to 1 decimal place, is ______________.Correct answer is '0.1'. Can you explain this answer?
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    A random variable X takes -1 and +1 with probabilities 0.2 and 0.8, respectively. It is transmitted across a channel which adds noise N, so that the random variable at the channel output is Y = X + N. The noise n is independent of X, and is uniformly distributed over the interval [-2, 2]. The receiver makes a decisionWhere the threshold θ ∈ [-1, 1] is chosen so as to minimize the probability of error Pr The minimum probability of error, rounded off to 1 decimal place, is ______________.Correct answer is '0.1'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 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 A random variable X takes -1 and +1 with probabilities 0.2 and 0.8, respectively. It is transmitted across a channel which adds noise N, so that the random variable at the channel output is Y = X + N. The noise n is independent of X, and is uniformly distributed over the interval [-2, 2]. The receiver makes a decisionWhere the threshold θ ∈ [-1, 1] is chosen so as to minimize the probability of error Pr The minimum probability of error, rounded off to 1 decimal place, is ______________.Correct answer is '0.1'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A random variable X takes -1 and +1 with probabilities 0.2 and 0.8, respectively. It is transmitted across a channel which adds noise N, so that the random variable at the channel output is Y = X + N. The noise n is independent of X, and is uniformly distributed over the interval [-2, 2]. The receiver makes a decisionWhere the threshold θ ∈ [-1, 1] is chosen so as to minimize the probability of error Pr The minimum probability of error, rounded off to 1 decimal place, is ______________.Correct answer is '0.1'. Can you explain this answer?.
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