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A perceptron has input weights $W_1=-3.9$ and $W_2=1.1$ with threshold value $T=0.3.$ What output does it give for the input $x_1=1.3$ and $x_2=2.2?$

  1. $-2.65$
  2. $-2.30$
  3. $0$
  4. $1$
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I am not getting the explanation. Can u plz explain it??
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w1*x1 + w2*x2 + . . . wn*xn

so -3.9*1.3 + 1.1*2.2

= -5.07+2.42

= - 2.65

Threshold T = 0.3

Now we compare the weighted sum -2.65 to the threshold 0.3.  Because -2.65 < 0.3, i.e. the weighted sum is less than the threshold, the output will be 0.

The neuron has a number of inputs x1, . . . , xn.  These inputs represent the incoming signals received from the neuron's synapses. So xi can either be  1, which corresponds to the presence of an incoming signal from the ith connection , or xi is 0, which corresponds to the absence of a signal from the ith connection.

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x1w1 + x2w2 = (1.3 x-3.9 ) + (2.2 x1.1 ) =  -2.65

Option (1) is correct.

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We need to compare Σ(Xi*Wi) with the threshold value and accordingly update the output of a function. This resulting value of a function determines the output of the neural network like 0 or 1, yes or no, -1 or +1.

Now here W1*X1 + W2*X2

=(-3.9*1.3)+(1.1*2.2)

=-2.65

which is <0.3 (the threshold value)

therefore output will be 0 and not -2.65. 

Hence the answer is Option B i.e., 0.

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According to given question w1 = – 3.9 and w2 = 1.1 and corresponding inputs are x1 = 1.3 and x2 = 2.2
so the output weight will be = w1 * x1 + w2 * x2
i.e. -3.9 * 1.3 + 1.1 * 2.2
= -5.07 + 2.42
= -2.65
Now we will compare the output weight -2.65 to the threshold 0.3.
-2.65 < 0.3
Then output will be zero.
So, option (C) will be correct.
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The output (\(y\)) of a perceptron is determined by the weighted sum of its inputs compared to a threshold. The formula for the output (\(y\)) of a perceptron is given by:

$y = \begin{cases} 1, & \text{if } \sum_{i} w_i x_i \geq T \\ 0, & \text{otherwise} \end{cases} $

where:
- \(w_i\) is the weight for the \(i\)-th input,
- \(x_i\) is the \(i\)-th input,
- \(T\) is the threshold.

Given the weights \(w_1 = -3.9\), \(w_2 = 1.1\), inputs \(x_1 = 1.3\), \(x_2 = 2.2\), and threshold \(T = 0.3\), we can calculate the weighted sum:

$\text{Weighted Sum} = w_1 \cdot x_1 + w_2 \cdot x_2 $

Substitute the values:

$\text{Weighted Sum} = (-3.9 \cdot 1.3) + (1.1 \cdot 2.2)$

Now, compare this with the threshold:

$\text{Weighted Sum} \geq T \,?$

If it's true, the output is 1; otherwise, the output is 0.

Let's calculate:

$\text{Weighted Sum} = (-5.07) + (2.42) \approx -2.65$

Now, compare with the threshold:

$-2.65 \geq 0.3 \,?$

This is not true, so the output is 0.

Therefore, the correct answer is:

$\textbf{C. 0}$
Answer:

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