An info source produces 0 and 1 with probabilities 0.3 and 0.7, respectively. the output of...
An info source produces 0 and 1 with probabilities 0.3 and 0.7, respectively. the output of the source is transmitted via a channel that has probabilities of error (turning a 1 into a 0 or a 0 into a 1) equal to 0.2
1) what is the probability that at the output a 1 is observed?
2) What is the probability that a 1 was output of the source if at the output of the channel a 1 is observed.
Homework Answers
Answer:
a)
Given,
To determine the probability that at the output a 1 is observed
i.e.,
= probability that 1 is produced and correctly transmitted + probability that 0 is produced and it is transmitted incorrectly
= 0.7 * (1 - 0.2) + 0.3 * 0.2
= 0.56 + 0.06
Required probability = 0.62
b)
Now to determine the probability that 1 was output of the source if
at the output of the channel a 1 is observed.
= 0.7*0.8/0.62
= 0.7 * 1.290323
= 0.903225806
= 0.9032
Add Answer to:
An info source produces 0 and 1 with probabilities 0.3 and 0.7,
respectively. the output of...
Information bits {0,1} are sent over binary symmetric communication channel with conditional probabilities P(YX) as shown...
Information bits {0,1} are sent over binary symmetric communication channel with conditional probabilities P(YX) as shown below. The priory probabilities of 0 and 1 are P(X=0)=0.3, P(X=1)=0.7. The error probability {=0.2. transmitter X 0 1-€ receiver Y 0 ៩ w 1-€ a) If 1 is transmitted, what are the probabilities of receiving 0 and 1? P(Y=0|X=1) and P(Y=1X=1) b) If 0 is received, what are the probabilities that 0 and 1 information bit is transmitted? P(X=0 Y=0) and P(X=1 Y=0)
4. An information source generates one of 4 possible levels namely -4, 0, 4, and 8 with equal probabilities. These levels are transmitted over a channel which adds Gaussian noise with zero means and...
4. An information source generates one of 4 possible levels namely -4, 0, 4, and 8 with equal probabilities. These levels are transmitted over a channel which adds Gaussian noise with zero means and variance of 1. The noise is independent of the signal. The receiver employs a ML decision rule. Clearly identify, the decision rules at the receiver and calculate the probability of error. -4 4
4. An information source generates one of 4 possible levels namely -4, 0,...
2. Consider a binary communication channel The probability that a transmitted 0 is received as 1 ...
2. Consider a binary communication channel The probability that a transmitted 0 is received as 1 is ε1- The probability that a transmitted 1 is received as 0 is Assume that the 2 transmitted inputs have equal probabilities. a) (10 points) Find the probability that the output received is 0. b) (10 points) Find the probability that the transmitted input is 0 given that the received output is 1 e) (5 points) Find the probability that the transmitted input is...
A data packet is transmitted over a lossy wireless channel with packet error rate 0.3. Most...
A data packet is transmitted over a lossy wireless channel with
packet error rate 0.3. Most communication systems adopt
the Automatic Repeat reQuest (ARQ) protocol. That is, if a packet
is successfully (with probability 0.7) or unsuccessfully
(with probability 0.3) received, the receiver respectively
sends a one-bit ‘ACK’ or ‘NAK’ message (over a separate feedback
channel) to the transmitter. After receiving an ‘ACK’, the
transmitter will move on to the next packet transmission;
otherwise, the transmitter will re-transmit the same...
8. There are three urns. Urnl contains 2 white and 3 black marbles, Urn2 contains 3...
8. There are three urns. Urnl contains 2 white and 3 black marbles, Urn2 contains 3 white and 2 black marbles, and Urn3 contains 1 white and 4 black marbles. First, the urn is selected equally likely, than a ball is drawn from the urn. a) We know that a white marble is chosen. What is the probability that the marble came from Urn2? b) We know that a black marble is chosen. What is the probability that the marble...
Consider a binary erasure channel, in which the input X ∼ Bernoulli ? (1 ?, 3)...
Consider a binary erasure channel, in which the input X ∼
Bernoulli ? (1 ?,
3)
and the output Y ∈ {0, e, 1} where the symbol e denotes an
erasure event (e appears when the channel is too “bad”). The
conditional distribution of Y given X is as follows:
pY |X (0|0) = 0.9, pY |X (e|0) = 0.1, pY |X (1|1) = 0.8, pY |X
(e|1) = 0.2.
Given that an erased symbol has been observed, i.e., Y...
1. You have three different coins where the probabilities of getting heads are 0.5, 0.7, and...
1. You have three different coins where the probabilities of getting heads are 0.5, 0.7, and 0.2 respectively You plan to flip each coin and count the total number of heads. You're curious what the probability of getting exactly two heads is. [1 point a. Explain why you cannot use the Binomial model for this situation. [3 points] b. Show that the probability of getting exactly two heads is 0.38. Define any events you want to use in words. c....
5. A binary Z-channel is show in the figure. Assume the input is "0" with probability...
5. A binary Z-channel is show in the figure. Assume the input is "0" with probability p and "1" with probability 1-p. (a) What can you say about the input bit if " is received? (b) Find the the probability that the input was "1" given that the output is "0" 0 Input Output 6. A transmitter randomly sends one of the messages in fa1, a2,.. ,an). The receiver either receives the transmitted message with probability p, or mistakenly receives...
ketch the graph of the probability density function over the indicated interval. 2x 9 [0, 3]...
ketch the graph of the probability density function over the indicated interval. 2x 9 [0, 3] y y 0.7 0.7 0.6 0.6 0.51 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 2 3 y у 0.7 0.7 0.6 0.6 0.5 0.54 0.4 0.41 0.3 0.3 0.2 0.2 y 0.71 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 2 Find the indicated probabilities. (a) PO < x < 2) (b) P(1 < x < 2)...
A random number generator will spread its output uniformly across the entire interval from 0 to...
A random number generator will spread its output uniformly across the entire interval from 0 to 1 as we allow it to generate a long sequence of numbers. The results of many trials are represented by the density curve of a uniform distribution. This density curve appears in red in the given figure. It has height 1 over the interval from 0 to 1, and height 0 everywhere else. The area under the density curve is 1: the area of...
Information bits {0,1} are sent over binary symmetric communication channel with conditional probabilities P(YX) as shown below. The priory probabilities of 0 and 1 are P(X=0)=0.3, P(X=1)=0.7. The error probability {=0.2. transmitter X 0 1-€ receiver Y 0 ៩ w 1-€ a) If 1 is transmitted, what are the probabilities of receiving 0 and 1? P(Y=0|X=1) and P(Y=1X=1) b) If 0 is received, what are the probabilities that 0 and 1 information bit is transmitted? P(X=0 Y=0) and P(X=1 Y=0)
4. An information source generates one of 4 possible levels namely -4, 0, 4, and 8 with equal probabilities. These levels are transmitted over a channel which adds Gaussian noise with zero means and variance of 1. The noise is independent of the signal. The receiver employs a ML decision rule. Clearly identify, the decision rules at the receiver and calculate the probability of error. -4 4
4. An information source generates one of 4 possible levels namely -4, 0,...
2. Consider a binary communication channel The probability that a transmitted 0 is received as 1 is ε1- The probability that a transmitted 1 is received as 0 is Assume that the 2 transmitted inputs have equal probabilities. a) (10 points) Find the probability that the output received is 0. b) (10 points) Find the probability that the transmitted input is 0 given that the received output is 1 e) (5 points) Find the probability that the transmitted input is...
A data packet is transmitted over a lossy wireless channel with
packet error rate 0.3. Most communication systems adopt
the Automatic Repeat reQuest (ARQ) protocol. That is, if a packet
is successfully (with probability 0.7) or unsuccessfully
(with probability 0.3) received, the receiver respectively
sends a one-bit ‘ACK’ or ‘NAK’ message (over a separate feedback
channel) to the transmitter. After receiving an ‘ACK’, the
transmitter will move on to the next packet transmission;
otherwise, the transmitter will re-transmit the same...
8. There are three urns. Urnl contains 2 white and 3 black marbles, Urn2 contains 3 white and 2 black marbles, and Urn3 contains 1 white and 4 black marbles. First, the urn is selected equally likely, than a ball is drawn from the urn. a) We know that a white marble is chosen. What is the probability that the marble came from Urn2? b) We know that a black marble is chosen. What is the probability that the marble...
Consider a binary erasure channel, in which the input X ∼
Bernoulli ? (1 ?,
3)
and the output Y ∈ {0, e, 1} where the symbol e denotes an
erasure event (e appears when the channel is too “bad”). The
conditional distribution of Y given X is as follows:
pY |X (0|0) = 0.9, pY |X (e|0) = 0.1, pY |X (1|1) = 0.8, pY |X
(e|1) = 0.2.
Given that an erased symbol has been observed, i.e., Y...
1. You have three different coins where the probabilities of getting heads are 0.5, 0.7, and 0.2 respectively You plan to flip each coin and count the total number of heads. You're curious what the probability of getting exactly two heads is. [1 point a. Explain why you cannot use the Binomial model for this situation. [3 points] b. Show that the probability of getting exactly two heads is 0.38. Define any events you want to use in words. c....
5. A binary Z-channel is show in the figure. Assume the input is "0" with probability p and "1" with probability 1-p. (a) What can you say about the input bit if " is received? (b) Find the the probability that the input was "1" given that the output is "0" 0 Input Output 6. A transmitter randomly sends one of the messages in fa1, a2,.. ,an). The receiver either receives the transmitted message with probability p, or mistakenly receives...
ketch the graph of the probability density function over the indicated interval. 2x 9 [0, 3] y y 0.7 0.7 0.6 0.6 0.51 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 2 3 y у 0.7 0.7 0.6 0.6 0.5 0.54 0.4 0.41 0.3 0.3 0.2 0.2 y 0.71 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 2 Find the indicated probabilities. (a) PO < x < 2) (b) P(1 < x < 2)...
Most questions answered within 3 hours.
-
Benning Inc is a defense contractor that uses job costing.
Because the firm uses a perpetual...
asked 29 minutes ago -
What is the net ionic equation for the reaction that would occur
when an aqueous solution...
asked 3 hours ago -
A
student bought $1000 worth of furniture. What is the equivalent
annual cost if it is...
asked 3 hours ago -
What taboo subject did Ida B. Wells suggest was consensual
between black men and white women?...
asked 5 hours ago -
You have just been hired by the EPA to help with the new gas
mileage standards...
asked 6 hours ago -
4) A firm is hit by increases in its wage rate, w.
a) How does this...
asked 6 hours ago -
A square current loop 5.4 cm on each side carries a 510 mA
current. The loop...
asked 8 hours ago -
What are five tips in conducting knowledge assessment/literature
review research? Each of these tips needs to...
asked 9 hours ago -
Antigen presenting cells link innate and adaptive immune
responses. In the theoretical scenario where phagosomes cannot...
asked 9 hours ago -
Dealing with conflict, in my opinion, is a skill and an art. I
believe that those...
asked 9 hours ago -
6. A long straight wire with circular cross section and radius
1.5 cm carries a 1.2...
asked 10 hours ago -
Deacon Corporation has provided the following financial data
from its balance sheet and income statement:
Year...
asked 10 hours ago