A message is coded in binary code consisting of two symbols : 0,1 ; the probabilities of transmission of the two symbols are 0.45 and 0.55 , respectively. In the channel of transmission the symbol 0 are distorted into 1's with a probability of 0.2 ; the 1's are distorted into 0's with a probability of 0.1 . Find the probability that
(a) a received 0 has not been distorted,
(b) a received 1 has been distorted.
Probability 20
2009-07-10 10:19 pm
回答 (2)
2009-07-10 10:49 pm
✔ 最佳答案
The probability of sending a zero is 0.45Out of this 0.45, 0.8 will be received as correct 0 = 0.45 x 0.8 = 0.36
Out of this 0.45, 0.2 will be received as incorrect 1 = 0.45 x 0.2 = 0.09
The probability of sending a one is 0.55
Out of this 0.55, 0.9 will be received as correct 1 = 0.55 x 0.9 = 0.495
Out of this 0.55, 0.1 will be received as incorrect 0 = 0.55 x 0.1 = 0.055
(a) a received 0 has not been distorted = 0.36/(0.36 + 0.055) = 0.867
(b) a received 1 has been distorted = 0.09/(0.09+0.495) = 0.154
2009-07-11 1:26 am
(a)
Pr (distortion | 0)
= Pr (distortion & 0) / Pr (0)
= [0.55 * 0.1) / [(0.55 * 0.1) + (0.45 * 0.8)]
= 0.055 / (0.055 + 0.36)
= 11 / 72
= 0.1528
(b)
Pr (distortion | 1)
= Pr (distortion & 1) / Pr (1)
= (0.45 * 0.2) / [(0.45 * 0.2) + (0.55 * 0.9)]
= 0.09 / (0.09 + 0.495)]
= 2 / 13
= 0.1538
2009-07-10 17:28:51 補充：
Sorry, for (a)
Pr (not distorted | 0)
= Pr (not distorted & 0) / Pr (0)
= (0.45 * 0.8) / [(0.55 * 0.1) + (0.45 * 0.8)]
= 0.36 / (0.055 + 0.36)
= 72 / 83
= 0.8675
Pr (distortion | 0)
= Pr (distortion & 0) / Pr (0)
= [0.55 * 0.1) / [(0.55 * 0.1) + (0.45 * 0.8)]
= 0.055 / (0.055 + 0.36)
= 11 / 72
= 0.1528
(b)
Pr (distortion | 1)
= Pr (distortion & 1) / Pr (1)
= (0.45 * 0.2) / [(0.45 * 0.2) + (0.55 * 0.9)]
= 0.09 / (0.09 + 0.495)]
= 2 / 13
= 0.1538
2009-07-10 17:28:51 補充：
Sorry, for (a)
Pr (not distorted | 0)
= Pr (not distorted & 0) / Pr (0)
= (0.45 * 0.8) / [(0.55 * 0.1) + (0.45 * 0.8)]
= 0.36 / (0.055 + 0.36)
= 72 / 83
= 0.8675
收錄日期: 2021-04-23 23:23:51
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