In the transmission of digital information, the probabilitythat a bit has high,

Question

In the transmission of digital information, the probabilitythat a bit has high, moderate or low distortion is 0.01, 0.04 and0.95, respectively. Suppose that three bits are transmittedand that the amount of distortion of each bit is assumedindependant. Let X and Y denote the number of bits with highand moderate distortion out of the three transmitted,respectively. Determine the following: a) What is the probability that two bits have high distortionand one has moderate distortion? b) What is the probability that all three bits have lowdistortion? c) The probability distribution mean and variance of X d) The conditional probability distribution, conditional meanand conditional variance of X give that Y=2. please show formulas In the transmission of digital information, the probabilitythat a bit has high, moderate or low distortion is 0.01, 0.04 and0.95, respectively. Suppose that three bits are transmittedand that the amount of distortion of each bit is assumedindependant. Let X and Y denote the number of bits with highand moderate distortion out of the three transmitted,respectively. Determine the following: a) What is the probability that two bits have high distortionand one has moderate distortion? b) What is the probability that all three bits have lowdistortion? c) The probability distribution mean and variance of X d) The conditional probability distribution, conditional meanand conditional variance of X give that Y=2. please show formulas

Explanation / Answer

Let H = 3, M = 2, and L =1 denote the events that a bit has high, moderate, andlow

x,y     fxy(x,y)

0,0    0.85738

0,1     0.1083

0,2   0.00456

0,3   0.000064

1,0   0.027075

1,1   0.00228

1,2  0.000048

2,0  0.000285

2,1  0.000012

3,0  0.000001

b)

x    fx(x)

0   0.970299

1   0.029835

2  0.000297

3  0.000001

y      fY|1(x)

0    0.09075

1    0.00764

y     fY|1(x)

0     0.920824

1    0.077543

2    0.001632

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