TABLE 5.1 TABLE OF THE Q-FUNCTION 0 5.000000e-01 2.4 8.197534e-03 4.8 7.933274e-07 0.1 4.601722e-01 2.5 6.209665e-03 4.9 4.791830e-07 0.2 4.207403e-01 2.6 4.661189e-03 5.0 2.866516e-07 0.3 3.820886e-01 2.7 3.466973e-03 5.1 1.698268e-07 0.4 3.445783e-01 2.8 2.555131e-03 5.2 9.964437e-06 0.5 3.085375e-01 2.9 1.865812e-03 5.3 5.790128e-08 0.6 2.742531e-01 3.0 1.349898e-03 5.4 3.332043e-08 0.7 2.419637e-01 3.1 9.676035e-04 5.5 1.898956e-08 0.8 2.118554e-01 3.2 6.871378e-04 5.6 1.071760e-08 0.9 1.840601e-01 3.3 4.834242e-04 5.7 5.990378e-09 1.0 1.586553e-01 3.4 3.369291e-04 5.8 3.315742e-09 1.1 1.356661e-01 3.5 2.326291e-04 5.9 1.817507e-09 1.2 1.150697e-01 3.6 1.591086e-04 6.0 9.865876e-10 1.3 9.680049e-02 3.7 1.077997e-04 6.1 5.303426e-10 1.4 8.075666e-02 3.8 7.234806e-05 6.2 2.823161e-10 1.5 6.680720e-02 3.9 4.809633e-05 6.3 1.488226e-10 1.6 5.479929e-02 4.0 3.167124e-05 6.4 7.768843e-11 1.7 4.456546e-02 4.1 2.065752e-05 6.5 4.016001e-11 1.8 3.593032e-02 4.2 1.334576e-05 6.6 2.055790e-11 1.9 2.871656e-02 4.3 8.539898e-06 6.7 1.042099e-11 2.0 2.275013e-02 4.4 5.412542e-06 6.8 5.230951e-12 2.1 1.786442e-02 4.5 3.397673e-06 6.9 2.600125e-12 2.2 1.390345e-02 4.6 2.112456e-06 7.0 1.279813e-12 2.3 1.072411e-02 4.7 1.300809e-06 Problem 2 The noise voltage in an electric circuit is modeled as a Gaussian random variable X with a mean equal to zero (m = 0) and a variance equal to 10-8 (0² = 10-8). a. What is the probability that the value of the noise exceeds 10-4? P(X > 10-4) = ? b. What is the probability that the noise value is between -2 × 10-4 and 10-4? P(−2 × 10-4 < x < 10¯4) = ?

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TABLE 5.1 TABLE OF THE Q-FUNCTION
0
5.000000e-01
2.4
8.197534e-03
4.8
7.933274e-07
0.1
4.601722e-01
2.5
6.209665e-03
4.9
4.791830e-07
0.2
4.207403e-01
2.6
4.661189e-03
5.0
2.866516e-07
0.3
3.820886e-01
2.7
3.466973e-03
5.1
1.698268e-07
0.4
3.445783e-01
2.8
2.555131e-03
5.2
9.964437e-06
0.5
3.085375e-01
2.9
1.865812e-03
5.3
5.790128e-08
0.6
2.742531e-01
3.0
1.349898e-03
5.4
3.332043e-08
0.7
2.419637e-01
3.1
9.676035e-04
5.5
1.898956e-08
0.8
2.118554e-01
3.2
6.871378e-04
5.6
1.071760e-08
0.9
1.840601e-01
3.3
4.834242e-04
5.7
5.990378e-09
1.0
1.586553e-01
3.4
3.369291e-04
5.8
3.315742e-09
1.1
1.356661e-01
3.5
2.326291e-04
5.9
1.817507e-09
1.2
1.150697e-01
3.6
1.591086e-04
6.0
9.865876e-10
1.3
9.680049e-02
3.7
1.077997e-04
6.1
5.303426e-10
1.4
8.075666e-02
3.8
7.234806e-05
6.2
2.823161e-10
1.5
6.680720e-02
3.9
4.809633e-05
6.3
1.488226e-10
1.6
5.479929e-02
4.0
3.167124e-05
6.4
7.768843e-11
1.7
4.456546e-02
4.1
2.065752e-05
6.5
4.016001e-11
1.8
3.593032e-02
4.2
1.334576e-05
6.6
2.055790e-11
1.9
2.871656e-02
4.3
8.539898e-06
6.7
1.042099e-11
2.0
2.275013e-02
4.4
5.412542e-06
6.8
5.230951e-12
2.1
1.786442e-02
4.5
3.397673e-06
6.9
2.600125e-12
2.2
1.390345e-02
4.6
2.112456e-06
7.0
1.279813e-12
2.3
1.072411e-02
4.7
1.300809e-06
Transcribed Image Text:TABLE 5.1 TABLE OF THE Q-FUNCTION 0 5.000000e-01 2.4 8.197534e-03 4.8 7.933274e-07 0.1 4.601722e-01 2.5 6.209665e-03 4.9 4.791830e-07 0.2 4.207403e-01 2.6 4.661189e-03 5.0 2.866516e-07 0.3 3.820886e-01 2.7 3.466973e-03 5.1 1.698268e-07 0.4 3.445783e-01 2.8 2.555131e-03 5.2 9.964437e-06 0.5 3.085375e-01 2.9 1.865812e-03 5.3 5.790128e-08 0.6 2.742531e-01 3.0 1.349898e-03 5.4 3.332043e-08 0.7 2.419637e-01 3.1 9.676035e-04 5.5 1.898956e-08 0.8 2.118554e-01 3.2 6.871378e-04 5.6 1.071760e-08 0.9 1.840601e-01 3.3 4.834242e-04 5.7 5.990378e-09 1.0 1.586553e-01 3.4 3.369291e-04 5.8 3.315742e-09 1.1 1.356661e-01 3.5 2.326291e-04 5.9 1.817507e-09 1.2 1.150697e-01 3.6 1.591086e-04 6.0 9.865876e-10 1.3 9.680049e-02 3.7 1.077997e-04 6.1 5.303426e-10 1.4 8.075666e-02 3.8 7.234806e-05 6.2 2.823161e-10 1.5 6.680720e-02 3.9 4.809633e-05 6.3 1.488226e-10 1.6 5.479929e-02 4.0 3.167124e-05 6.4 7.768843e-11 1.7 4.456546e-02 4.1 2.065752e-05 6.5 4.016001e-11 1.8 3.593032e-02 4.2 1.334576e-05 6.6 2.055790e-11 1.9 2.871656e-02 4.3 8.539898e-06 6.7 1.042099e-11 2.0 2.275013e-02 4.4 5.412542e-06 6.8 5.230951e-12 2.1 1.786442e-02 4.5 3.397673e-06 6.9 2.600125e-12 2.2 1.390345e-02 4.6 2.112456e-06 7.0 1.279813e-12 2.3 1.072411e-02 4.7 1.300809e-06
Problem 2
The noise voltage in an electric circuit is modeled as a Gaussian random variable X with a mean
equal to zero (m = 0) and a variance equal to 10-8 (0² = 10-8).
a. What is the probability that the value of the noise exceeds 10-4? P(X > 10-4) = ?
b. What is the probability that the noise value is between -2 × 10-4 and 10-4?
P(−2 × 10-4 < x < 10¯4) = ?
Transcribed Image Text:Problem 2 The noise voltage in an electric circuit is modeled as a Gaussian random variable X with a mean equal to zero (m = 0) and a variance equal to 10-8 (0² = 10-8). a. What is the probability that the value of the noise exceeds 10-4? P(X > 10-4) = ? b. What is the probability that the noise value is between -2 × 10-4 and 10-4? P(−2 × 10-4 < x < 10¯4) = ?
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