A message consists of a string of bits (0s and 1s). Due to noise in the communications channel, each bit has probability 0.3 of being reversed (i.e., a 1 will be changed to a 0 or a 0 to a 1). To improve the accuracy of the communication, each bit is sent five times, so, for example, 0 is sent as 00000. The receiver assigns the value 0 if three or more of the bits are decoded as 0, and 1 if three or more of the bits are decoded as 1. Assume that errors occur independently.
a. A 0 is sent (as 00000). What is the probability that the receiver assigns the correct value of 0?
b. Assume that each bit is sent n times, where n is an odd number, and that the receiver assigns the value decoded in the majority of the bits. What is the minimum value of n necessary so that the probability that the correct value is assigned is at least 0.90?
(a) Let X be the number of bits that are reversed. Then X~ Bin(5,0.3). The correct value is assigned if X 2.
(b) We need to find the smallest odd value of n so that P(X?(n -1)/2) 0.90 when X~ Bin(n, 0.3). Consulting Table A.1, we find that if n = 3, P(X?1) = 0.784, if n = 5, P(X?2) = 0.837, if n = 7, P(X?3) = 0.874, and if n = 9, P(X?4) = 0.901. The smallest value of n is therefore n = 9.
You might also like to view...
Which type of dimensioning offers the best way to eliminate tolerance accumulation?
A. direct B. chain C. baseline D. unilateral
The major problem that faces welders when welding pipe in the ____ position is that the area to be welded is often located in corners, and reaching the back side of the weld is difficult.
A. 6G 45 degree inclined B. 2G vertical fixed C. 5G horizontal fixed D. 1G horizontal rolled
Some ways to prevent chatter when cutting off material with a parting tool are to use:
A) A heavy feed, low speed and cut off the material near the chuck or near the tailstock center B) Coolant, feed in very slowly and use very high speed C) A light hand feed, low speed that makes a chip, low speed, cutting oil and a rigid setup D) Diagonally ground parting tools, use heavy power feed and a high speed
You can stretch a polyline by selecting one of the revealed grips and move it to any point in the 3D space
Indicate whether the statement is true or false