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author | Trupti Kini | 2016-02-10 23:30:29 +0600 |
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committer | Trupti Kini | 2016-02-10 23:30:29 +0600 |
commit | 148e58d03cf168dbed05a44bf368977619abe09b (patch) | |
tree | 9ad80918c7091afbeeb4650ea3d7cf1c2f103e91 /Analog_and_Digital_Communications_by_H_P_Hsu/CHAPTER06.ipynb | |
parent | 81c47daafaef162197958c24fa065c2b2c3e6413 (diff) | |
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Added(A)/Deleted(D) following books
A Analog_and_Digital_Communications_by_H_P_Hsu/CHAPTER01.ipynb
A Analog_and_Digital_Communications_by_H_P_Hsu/CHAPTER03.ipynb
A Analog_and_Digital_Communications_by_H_P_Hsu/CHAPTER04.ipynb
A Analog_and_Digital_Communications_by_H_P_Hsu/CHAPTER05.ipynb
A Analog_and_Digital_Communications_by_H_P_Hsu/CHAPTER06.ipynb
A Analog_and_Digital_Communications_by_H_P_Hsu/CHAPTER08.ipynb
A Analog_and_Digital_Communications_by_H_P_Hsu/CHAPTER09.ipynb
A Analog_and_Digital_Communications_by_H_P_Hsu/CHAPTER10.ipynb
A Analog_and_Digital_Communications_by_H_P_Hsu/CHAPTER11.ipynb
A Analog_and_Digital_Communications_by_H_P_Hsu/screenshots/Screenshot04.png
A Analog_and_Digital_Communications_by_H_P_Hsu/screenshots/Screenshot08.png
A Analog_and_Digital_Communications_by_H_P_Hsu/screenshots/Screenshot10.png
A Basic_electrical_and_electronics_engineering_-1_by_S_K_Bhattacharya_and_debasish_de/CHAPTER01.ipynb
A Basic_electrical_and_electronics_engineering_-1_by_S_K_Bhattacharya_and_debasish_de/CHAPTER02.ipynb
A Basic_electrical_and_electronics_engineering_-1_by_S_K_Bhattacharya_and_debasish_de/CHAPTER03.ipynb
A Basic_electrical_and_electronics_engineering_-1_by_S_K_Bhattacharya_and_debasish_de/CHAPTER04.ipynb
A Basic_electrical_and_electronics_engineering_-1_by_S_K_Bhattacharya_and_debasish_de/CHAPTER05.ipynb
A Basic_electrical_and_electronics_engineering_-1_by_S_K_Bhattacharya_and_debasish_de/CHAPTER06.ipynb
A Basic_electrical_and_electronics_engineering_-1_by_S_K_Bhattacharya_and_debasish_de/CHAPTER07.ipynb
A Basic_electrical_and_electronics_engineering_-1_by_S_K_Bhattacharya_and_debasish_de/CHAPTER08.ipynb
A Basic_electrical_and_electronics_engineering_-1_by_S_K_Bhattacharya_and_debasish_de/screenshots/Screenshot02.png
A Basic_electrical_and_electronics_engineering_-1_by_S_K_Bhattacharya_and_debasish_de/screenshots/Screenshot04.png
A Basic_electrical_and_electronics_engineering_-1_by_S_K_Bhattacharya_and_debasish_de/screenshots/Screenshot06.png
A Power_System_Operation_and_Control_by_B._R._Gupta/Chapter1.ipynb
A Power_System_Operation_and_Control_by_B._R._Gupta/Chapter2.ipynb
A Power_System_Operation_and_Control_by_B._R._Gupta/Chapter3.ipynb
A Power_System_Operation_and_Control_by_B._R._Gupta/Chapter4.ipynb
A Power_System_Operation_and_Control_by_B._R._Gupta/Chapter5.ipynb
A Power_System_Operation_and_Control_by_B._R._Gupta/Chapter6.ipynb
A Power_System_Operation_and_Control_by_B._R._Gupta/screenshots/Ch1-EnergyLadCurveAndMassCurve.png
A Power_System_Operation_and_Control_by_B._R._Gupta/screenshots/Ch2-LoadGeneration.png
A Power_System_Operation_and_Control_by_B._R._Gupta/screenshots/Ch2-ReceivedPower.png
Diffstat (limited to 'Analog_and_Digital_Communications_by_H_P_Hsu/CHAPTER06.ipynb')
-rw-r--r-- | Analog_and_Digital_Communications_by_H_P_Hsu/CHAPTER06.ipynb | 380 |
1 files changed, 380 insertions, 0 deletions
diff --git a/Analog_and_Digital_Communications_by_H_P_Hsu/CHAPTER06.ipynb b/Analog_and_Digital_Communications_by_H_P_Hsu/CHAPTER06.ipynb new file mode 100644 index 00000000..3fe5c8b4 --- /dev/null +++ b/Analog_and_Digital_Communications_by_H_P_Hsu/CHAPTER06.ipynb @@ -0,0 +1,380 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:a14c7a989e8c3ea4932d8ef52a48aca6495d802f38f7487ab2fe14fa0d728058"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "CHAPTER06:PROBABILITY AND RANDOM VARIABLES"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example E07 : Pg 6.16"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Page Number: 6.16\n",
+ "# Example 6.7\n",
+ "# Given\n",
+ "# Pdot=2*Pdash and Pdot+Pdash=1\n",
+ "# Therfore, on solving using linear equations\n",
+ "import math \n",
+ "#a=([1, -2],[1, 1]);\n",
+ "##c=([0],[1]);\n",
+ "#b=1/(a)*c;\n",
+ "Pdash=0.3333333;#b(1,1);\n",
+ "Pdot=0.6666667;#b(2,1);\n",
+ "print'Pdot:',Pdot\n",
+ "print'Pdash:',Pdash"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Pdot: 0.6666667\n",
+ "Pdash: 0.3333333\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example E14 : Pg 6.18"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Page Number: 6.18\n",
+ "# Example 6.14\n",
+ "# Given\n",
+ "p=0.1;\n",
+ "q=0.2;\n",
+ "Pm0=0.5;\n",
+ "Pr1bym0=p;\n",
+ "Pr0bym1=q;\n",
+ "# (a) Find Pr0 and Pr1\n",
+ "Pm1=1-Pm0;\n",
+ "Pr0bym0=1-Pr1bym0;\n",
+ "Pr1bym1=1-Pr0bym1;\n",
+ "\n",
+ "# By formula\n",
+ "# P(r0)=(P(r0/m0)*P(m0))+(P(r0/m1)*P(m1);\n",
+ "# P(r1)=(P(r1/m0)*P(m0))+(P(r1/m1)*P(m1);\n",
+ "Pr0=(Pr0bym0*Pm0)+(Pr0bym1*Pm1);\n",
+ "Pr1=(Pr1bym0*Pm0)+(Pr1bym1*Pm1);\n",
+ "print'P(r0):',Pr0\n",
+ "print'P(r1):',Pr1\n",
+ "# (b)P(m0/r0)\n",
+ "# Using Bayes Rule\n",
+ "# P(m0/r0)=(P(m0)*P(r0/m0)/P(r0))\n",
+ "Pm0byr0=(Pm0*Pr0bym0)/Pr0;\n",
+ "print'P(m0/r0):',Pm0byr0\n",
+ "# (c)P(m1/r1)\n",
+ "# Using Bayes Rule\n",
+ "# P(m1/r1)=(P(m1)*P(r1/m1)/P(r1))\n",
+ "Pm1byr1=(Pm1*Pr1bym1)/Pr1;\n",
+ "print'P(m1/r1):',Pm1byr1\n",
+ "\n",
+ "# (d)Probabilty error\n",
+ "# As Pe=(P(r1/m0)*P(m0))+(P(r0/m1)*P(m1))\n",
+ "Pe=(Pr1bym0*Pm0)+(Pr0bym1*Pm1);\n",
+ "print'Probability error:',Pe\n",
+ "\n",
+ "# (e)Probabilty that is transmitted correctly\n",
+ "# As Pc=(P(r0/m0)*P(m0))+(Pr1bym1*Pm1)\n",
+ "\n",
+ "Pc=(Pr0bym0*Pm0)+(Pr1bym1*Pm1);\n",
+ "print'Probabilty that is transmitted correctly:',Pc"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "P(r0): 0.55\n",
+ "P(r1): 0.45\n",
+ "P(m0/r0): 0.818181818182\n",
+ "P(m1/r1): 0.888888888889\n",
+ "Probability error: 0.15\n",
+ "Probabilty that is transmitted correctly: 0.85\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example E16 : Pg 6.21"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Page Number: 6.21\n",
+ "# Example 6.16\n",
+ "# Given\n",
+ "p=0.4;\n",
+ "Pp=p;\n",
+ "q=0.3;\n",
+ "Pn=q;\n",
+ "a=1.; # i start value\n",
+ "b=6.; # i end value\n",
+ "# (a)Probabilty that all pulses are positive\n",
+ "s=1.;\n",
+ "for i in range(1,6):\n",
+ " s=s*Pp;\n",
+ "print'Probabilty that all pulses are positive:',s\n",
+ "\n",
+ "# (b)Pulses are positive ,positive, positive, zero,zero,negative\n",
+ "Pz=1.-(p+q);\n",
+ "s1=(Pp**3.)*(Pz**2.)*Pn;\n",
+ "print'Probabilty that all pulses are positive ,positive, positive, zero,zero,negative:',s1"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Probabilty that all pulses are positive: 0.01024\n",
+ "Probabilty that all pulses are positive ,positive, positive, zero,zero,negative: 0.001728\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example E17 : Pg 6.21"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Page Number: 6.21\n",
+ "# Example 6.17\n",
+ "# Given\n",
+ "import math \n",
+ "P1=0.6;\n",
+ "P0=0.4;\n",
+ "n=5.; # Five digit sequence\n",
+ "j=2.; # two outcomes 0 and 1\n",
+ "\n",
+ "# (a)1,1,0,0,0\n",
+ "xf=(math.factorial(n))/((math.factorial(j))*(math.factorial(n-j)));\n",
+ "s=xf*(P1**j)*(P0**(n-j));\n",
+ "print'Probability for 1,1,0,0,0:',s\n",
+ "\n",
+ "# (b)atleast 3 1's\n",
+ "# P(X>=3)=1-P(X<=2)\n",
+ "# Here y=1-x\n",
+ "x=0;\n",
+ "for k in range(0,2):\n",
+ " f=(math.factorial(n))/((math.factorial(k))*(math.factorial(n-k)));\n",
+ " x=x+(f*((P1**k)*(P0**(n-k))));\n",
+ "y=1.-x;\n",
+ "print'Probability for atleast three 1 s:',y"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Probability for 1,1,0,0,0: 0.2304\n",
+ "Probability for atleast three 1 s: 0.91296\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example E20 : Pg 6.23"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Page Number: 6.23\n",
+ "# Example 6.20\n",
+ "# Given\n",
+ "import math \n",
+ "pe=0.01; # Error probability\n",
+ "\n",
+ "# (a) Probabilty of more than one error in 10 recieved digits\n",
+ "n=10.;\n",
+ "# As P(X>1)=1-P(X=0)-P(X=1)\n",
+ "# Let x=P(X>1)\n",
+ "# s=P(X=0)+P(X=1)\n",
+ "s=0;\n",
+ "for t in range(0,1):\n",
+ " f=(math.factorial(n))/((math.factorial(t))*(math.factorial(n-t)));\n",
+ " s=s+(f*(pe**t)*((1-pe)**(n-t)));\n",
+ "x=1-s;\n",
+ "print'Probabilty of more than one error in 10 recieved digits:',x\n",
+ "\n",
+ "# (b)Using Poisson approximation\n",
+ "# P(X=k)~[{(%exp)**(-n*p)}*{((n*p)**k)}]/k factorial\n",
+ "s1=0;\n",
+ "for k in range(0,1):\n",
+ " j=math.factorial(k);\n",
+ " s1=s1+((math.exp(-n*pe))*(((n*pe)**k)))/j;\n",
+ "x1=1.-s1;\n",
+ "print'Using Poisson Approximation:',x1"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Probabilty of more than one error in 10 recieved digits: 0.0956179249912\n",
+ "Using Poisson Approximation: 0.095162581964\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example E23 : Pg 6.23"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Page Number: 6.23\n",
+ "# Example 6.23\n",
+ "# We find, k=1/(b-a)\n",
+ "# (b) if a=1 and b=2,P(|x|<c) where c=1/2\n",
+ "a=-1.;\n",
+ "b=2.;\n",
+ "c=1./2.;\n",
+ "\n",
+ "k=1./(b-a);\n",
+ "# P(|x|<c) = P(-c<=x<=c)\n",
+ "# Let y\n",
+ "x0=-c;x1=c;\n",
+ "y=1.;#integrate('1','x',x0,x1);\n",
+ "y1=k*y;\n",
+ "print'P(|x|<c):',y1"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "P(|x|<c): 0.333333333333\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example E41 : Pg 6.34"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Page Number: 6.34\n",
+ "# Example 6.41\n",
+ "# Given\n",
+ "import math \n",
+ "n=16.; # binary digits\n",
+ "p=0.01; # Probabilty error due to noise\n",
+ "\n",
+ "# (a) Average errors per block\n",
+ "# E(X)=n*p\n",
+ "EofX=n*p;\n",
+ "print'Average errors per block:',EofX\n",
+ "\n",
+ "# (b)Varience of errors of block\n",
+ "# s=n*p*(1-p)\n",
+ "s=n*p*(1.-p);\n",
+ "print'Varience of errors per block:',s\n",
+ "\n",
+ "\n",
+ "# (c) Probability that number of errors per block is bgeater or equal than 4\n",
+ "i=4.;\n",
+ "# AsP(X>=4)=1=P(X<=3)\n",
+ "P3=0;\n",
+ "for k in range(0,3):\n",
+ " f=(math.factorial(n))/((math.factorial(k))*(math.factorial(n-k)));\n",
+ " P3=P3+(f*(p**k)*((1-p)**(n-k)));\n",
+ "P4=1.-P3;\n",
+ "print'Probability that number of errors per block is bgeater or equal than 4:',P4"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Average errors per block: 0.16\n",
+ "Varience of errors per block: 0.1584\n",
+ "Probability that number of errors per block is bgeater or equal than 4: 0.000507942409291\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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