A binary message m, where m is equal either to 0 or to 1, is sent over an information channel. Assume that if m = 0, the value s = −1. 5 is sent, and if m = 1, the value s = 1. 5 is sent. The value received is X, where X = s + E, and E ∼ N(0, 0. 64). If X ≤ 0. 5, then the receiver concludes that m = 0, and if X > 0. 5, then the receiver concludes that m = 1
Answers
The probability of error is approximately 0.0559.
This scenario is an example of binary communication with additive white Gaussian noise (AWGN) channel. The sender is sending a binary message m, and the receiver is receiving a noisy version of the message X. The noise is assumed to be Gaussian with zero mean and variance 0.64.
To decode the message, the receiver checks whether X is less than or equal to 0.5. If it is, the receiver concludes that the original message was 0, otherwise the receiver concludes that the original message was 1.
Let's compute the probability of error for this system. The probability of error is the probability that the receiver makes an incorrect decision about the original message given the received value X.
If the original message was 0 and the received value X is greater than 0.5, then the receiver will make an error and conclude that the message was 1. The probability of this error is given by:
P(error | m=0) = P(X > 0.5 | m=0)
= P(s + E > 0.5 | m=0)
= P(E > 2.0 | m=0) [since s = -1.5 when m=0]
= 1 - P(E <= 2.0 | m=0)
= 1 - Φ(2.0/0.8) [since E ~ N(0, 0.64)]
= 1 - Φ(2.5)
= 0.0062
where Φ is the cumulative distribution function of the standard normal distribution.
Similarly, if the original message was 1 and the received value X is less than or equal to 0.5, then the receiver will make an error and conclude that the message was 0. The probability of this error is given by:
P(error | m=1) = P(X <= 0.5 | m=1)
= P(s + E <= 0.5 | m=1)
= P(E <= -1.0 | m=1) [since s = 1.5 when m=1]
= Φ(-1.25) [since E ~ N(0, 0.64)]
= 0.1056
The overall probability of error is the weighted average of these two error probabilities, weighted by the probabilities of the two possible messages:
P(error) = P(error | m=0) * P(m=0) + P(error | m=1) * P(m=1)
= 0.0062 * 0.5 + 0.1056 * 0.5
= 0.0559
Therefore, the probability of error for this system is approximately 0.0559.
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Related Questions
what is the product of (5.1x10^3)x(3.2x10^3)
Answers
Answer:
Step-by-step explanation:
0 is the answer
Ms. Smith puts a variety of wrapped chocolate candies into a bag. There are 5 silver-wrapped candies, 1 purple-wrapped candy, 2 striped candies, and 4 gold-wrapped candies. If 15 students select one candy at a time out of the bag without looking, and replace the candy after each draw, how many students would be expected to select a gold-wrapped candy from the bag?
Answers
Therefore , the solution of the given problem of unitary method comes out to be in a group of 15, we would anticipate that 5 pupils would choose a candy.
Unitary method: what is it?To finish a job using the unitary method, divide the lengths of just this minute subsection by two. In a nutshell, the unit method eliminates a desired item from both the characterized by a set and colour subsets. 40 pens, for instance, will cost Rupees ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait. There are changes and unanswered issues (mathematics, algebra).
Here,
There are a total of 12 sweets in the bag: 5 + 1 + 2 + 4 candies. Given that there are 4 gold-wrapped candies out of a total of 12, the chance of choosing one during any given draw is 4/12 = 1/3.
. Therefore, regardless of how many draws have been conducted before, the chance of choosing a gold-wrapped treat is always 1/3.
In a class of 15 pupils, the predicted proportion of students who would choose a gold-wrapped treat would be:
Expected number of gold-wrapped candies = (1/3) * (number of draws) * (probability of choosing gold-wrapped candy on one draw) = 5
Therefore, in a group of 15, we would anticipate that 5 pupils would choose a candy that was wrapped in gold.
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X=
58
43
71
no bots fr
Answers
Answer:
A
Step-by-step explanation:
upgrading a certain software package requires installation of 68 new files. files are installed consecutively. the installation time is random, but on the average, it takes 15 sec to install one file, with a variance of 11 sec2. (a) what is the probability that the whole package is upgraded in less than 12 minutes? (b) a new version of the package is released. it requires only n new files to be installed, and it is promised that 95% of the time upgrading takes less than 10 minutes. given this information, compute n.
Answers
Therefore, upgrading the new version of the package requires installation of 18 new files.
What are quadratic equations?A quadratic equation is a type of polynomial equation in one variable (usually denoted by "x") where the highest exponent of the variable is 2. The general form of a quadratic equation is:
\(ax^2 + bx + c = 0\)
where a, b, and c are constants (numbers) and a is not equal to zero.
The solutions to a quadratic equation can be found by using the quadratic formula:
\(x = (-b ±\sqrt(b^2-4ac))/2a\)
by the question.
a) Let X be the time it takes to install the entire package. We know that X follows a normal distribution with mean μ = 1568 = 1020 seconds and variance σ^2 = 1168 = 748. We want to find the probability that X is less than 720 seconds (12 minutes).
Using the standard normal distribution, we can standardize X as follows:
\(Z = (X - μ) / σ = (720 - 1020) /\sqrt(748) = -4.05\)
Using a standard normal table or a calculator, we find that the probability of Z being less than -4.05 is approximately 3.3x10^-5. Therefore, the probability of upgrading the entire package in less than 12 minutes is approximately 3.3x10^-5.
(b) Let Y be the time it takes to install n files. We want to find the value of n such that upgrading takes less than 10 minutes with 95% probability.
We know that Y follows a normal distribution with mean μ = 15n and variance σ^2 = 11n. We want to find the value of n such that P(Y < 600) = 0.95.
Using the standard normal distribution and standardizing Y, we have:
\(Z = (Y - μ) / σ = (600 - 15n) /\sqrt(11n)\)
We want to find the value of n such that P (Z < z) = 0.95, where z is the z-score that corresponds to the 95th percentile. From a standard normal table or a calculator, we find that z ≈ 1.645. Therefore, we have:
(600 - 15n) / sqrt(11n) = 1.645
Squaring both sides and rearranging, we get:
\(11n^2 - 196n + 3600 = 0\)
Solving this quadratic equation, we get two solutions: n ≈ 17.17 and n ≈ 31.44. Since we want a positive integer value for n, the only valid solution is n = 18.
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m∠GEF = 40º. What is the measure of its supplement?
Answers
The measure of the supplement of angle GEF is calculated as: 140 degrees.
What is the Supplement of an Angle?The supplement of an angle is the angle that, when added to the original angle, forms a straight line or 180 degrees. In other words, the supplement of an angle is the angle that completes the original angle to make it a straight angle.
For example, if the original angle is 30 degrees, then the supplement of that angle is 150 degrees, because 30 + 150 = 180. Similarly, if the original angle is 75 degrees, then the supplement of that angle is 105 degrees, because 75 + 105 = 180.
Given that the measure of angle GEF is 40°, to find the measure of the supplement of angle GEF, subtract 40 from 180.
Therefore:
The measure of the supplement of angle GEF = 180 - 40
= 140 degrees.
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If X is correlated with Y, what must be true about X and Y? Explain your reasoning. a. A corelation exists between two variables when both variables increase together b. Increasing values of X go with either increasing or decreasing values of Y. A comelation exists between two variables when both variables increase or decrease together c. Increasing values of X go with either increasing or deoreasing values of Y. A correlation exiss between X and Y when higher values of X consistently go with higher values of Y or when higher values of X consistently go with lower values of Y d. X causes Y. If Y decreases as X increases, then X must cause Y to change. e. Increasing values of X go with increasing values of Y. A correlation exists between two variables when both viariables decrease togetherf. X causes Y. If Y increases as X increases, then X must cause Y to change-
Answers
Answer:
it is a statistical measure of the relationship between two variables that indicates the extent to which the variables change together in the same or opposite direction. Correlation does not imply causation, meaning that a correlation between two variables does not necessarily mean that one variable causes the other.
Based on this definition, the correct answer is b. Increasing values of X go with either increasing or decreasing values of Y. A correlation exists between two variables when both variables increase or decrease together. This statement captures the idea that correlation can be positive or negative, and that it reflects a linear relationship between two variables.
Step-by-step explanation:
a is wrong because it only describes positive correlation, not negative correlation.
c is wrong because it confuses correlation with consistency. Correlation does not require that higher values of X always go with higher or lower values of Y, only that they tend to do so on average.
d and f are wrong because they assume causation from correlation, which is a logical fallacy.
e is wrong because it contradicts itself. It says that increasing values of X go with increasing values of Y, which is positive correlation, but then it says that a correlation exists when both variables decrease together, which is negative correlation.
If X is correlated with Y, it implies a predictive statistical relationship between X and Y. This correlation can be positive or negative implying respective increase or decrease in values of both variables. But, this correlation doesn't prove causation.
Explanation:If X is correlated with Y, it indicates a statistical relationship between the two variables, X and Y. This relationship can be positive or negative. If it is a positive correlation, as X increases, Y will also increase and similarly, as X decreases, Y will also decrease. Contrarily, in a negative correlation, as X increases, Y decreases and vice versa. However, it is important to understand that correlation does not imply causation. That is, if X and Y are correlated, it does not necessarily mean that changes in X cause changes in Y or vice versa. It only means that they move in a predictable manner relative to each other.
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If P is the midpoint of ST, SP = x + 4, and ST = 4x, determine the length of ST.
Answers
The length of ST is 16 units.
What is Line segment?A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.
We have to given that;
Point P is the midpoint of ST.
SP = x + 4, and ST = 4x
Since, P is the midpoint of ST.
Hence, We get;
⇒ SP = PT
And, ST = 2 SP
Substitute all values we get;
⇒ 4x = 2 (x + 4)
⇒ 4x = 2x + 8
⇒ 4x - 2x = 8
⇒ 2x = 8
⇒ x = 4
Thus, The value of ST = 4x
= 4×4
= 16
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A circle has a circumference of 3 meters. What is the circle's radius?
Use 3.14 for pi and round your answer to the nearest tenth.
PLS HELP!!! No links pls and ty <3
Answers
Formula for the circumference of a circle = pi x 2 x radius
Circumference = 3
pi = 3.14
radius = r
---To find the radius, we will need to solve for it. Start by plugging in what we know.
3 = 3.14 x 2 x r
---Simplify by multiplying 3.14 by 2
3 = 6.28 x r
---Divide both sides by 6.28 to solve for r
r = 3 / 6.28 = 0.4777
---Round the decimal to the nearest tenth
r = 0.5
Hope this helps!
r=0.5
Solution:Circumference of a circle - C=2πrPlug in the values we are given:3=2πrSimplify:3=6.3rDivide both sides by 6.3:r=0.5Hope it helps.
Do comment if you have any query.
what are the factors of 64 that have a sum of 16
Answers
Anwnser 8
Step-by-step explanation:
2,4,6,8,32
The midpoint of AB is M(4,-2). If the coordinates of A are (3, -6), what are the
coordinates of B?
Answers
Answer:
okay here we go
Step-by-step explanation:
\(in \: vectos \: ab \: means \: ob - oa \\ but \: the \: midpoint \: m \: is \: equal \: to \: a \: half \: of \: ab \\ \\ therefore \: m = \frac{1}{2} ab \\ = \frac{1}{2} (ob - oa) \\ = \frac{1}{2} (ob - (3. - 6)) \\ (4. - 2) = \frac{1}{2} (ob - (3. - 6)) \\ (8. - 4) = (ob - (3. - 6)) \\ ob = (11. - 2)\)
calculate the value of 2a+3b if a=1 and b=2
Answers
calculate the value of 2a+3b if a=1 and b=2
= 2 * 1 + 3 * 2
= 2 + 6
= 8
* = multiply by
2a = 2 * a
and 3b = 3 * b
The school office bought 25 pounds of paper . One pound of paper contains 800 sheets of paper did the school buy ?
Answers
Answer:
I think 20,000 sheets of paper
Step-by-step explanation:
800 x 25 is 20,000
Answer:
The school has 20,000 sheets of paper.
Step-by-step explanation:
800 sheets in one pound
800X25=20,000
i was doing fine until i came to this question please help
i dont know what its asking
Answers
6x-9=4x+3
Add 9 to both sides
It becomes
6x=4x+9
Then subtract 4x
It becomes 2x=12
Divide 2 by both sides
It becomes
X=12 divided by 2
Which of course is 6
X=6
The average of the squared distanced of the data values from the mean.
Answers
The average of the squared distances of the data values from the mean is known as the variance.
Variance is a statistical measure that quantifies the spread or dispersion of a dataset. It is calculated by taking the mean of the squared differences between each data point and the mean of the dataset. By squaring the differences, the negative values are eliminated, and the distances from the mean are emphasized. The resulting variance value provides insights into how closely the data points are clustered around the mean. A larger variance indicates a wider spread of data points, while a smaller variance suggests a more concentrated distribution. Variance is commonly used in various fields, including finance, physics, and social sciences, to analyze and compare datasets.
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Period
- Date
4. Open Response The ratio of Braydon's
number of laps he ran to the time he ran is
6:2. The ratio of Monique's number of laps
she ran to the time she ran is 10: 4. Explain
why these ratios are not in a proportional
relationship. (Lesson 2)
Answers
Answer:
(Some textbooks describe a proportional relationship by saying that " y varies proportionally with x " or that " y is directly proportional to x .") This means that as x increases, y increases and as x decreases, y decreases-and that the ratio between them always stays the same.
10:4 = 5:2
6:2 = 3:1
Not equal.
Grey went out out for breakfast and had pancake for $5. 95 sausage for $1. 50, and orange juice for $2. 25. He would like to tip the waiter 12% of the total price. How much is his total including the tip?
Answers
Total cost of breakfast = $9.70, Tip = $1.16, Total cost including tip = $10.86.
To find the total bill including the tip, we first need to calculate the total cost of the breakfast, which is the sum of the pancake, sausage, and orange juice prices. Adding these up, we get $5.95 + $1.50 + $2.25 = $9.70.
Next, we need to calculate the tip, which is 12% of the total cost. Multiplying the total cost by 0.12, we get $9.70 x 0.12 = $1.16.
Finally, to find the total bill including the tip, we add the total cost and the tip amount: $9.70 + $1.16 = $10.86.
Therefore, Grey's total bill including the tip is $10.86.
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Use < , > , or = to compare the set of real numbers.
√ 6
√ 2
Answers
Answer:
sqrt(6) > sqrt(2)
Step-by-step explanation:
A weather forecaster predicts that the May rainfall in a local area will be between three and six inches but has no idea where within the interval the amount will be. Let x be the amount of May rainfall in the local area, and assume that x is uniformly distributed over the interval three to six inches. (a) Write the formula for the probability curve of x. f(x) = / for < x < (b) What is the probability that May rainfall will be at least four inches? At least five inches?
Answers
The probability that May rainfall will be at least five inches can be calculated as: P(x ≥ 5) = (6-5) / (6-3) = 1/3
(a) The formula for the probability curve of x is:
f(x) = 1 / (6-3) = 1/3 for 3 ≤ x ≤ 6
This is because x is uniformly distributed over the interval three to six inches, which means that all values within the interval are equally likely to occur. The probability of any specific value of x occurring is therefore equal to the width of the interval (6-3 = 3) divided by the total length of the interval, which is 1/3.
(b) The probability that May rainfall will be at least four inches can be calculated as follows:
P(x ≥ 4) = (6-4) / (6-3) = 2/3
This is because the probability of x being greater than or equal to 4 is equal to the width of the interval from 4 to 6 (which is 6-4 = 2) divided by the total length of the interval (which is 6-3 = 3).
This is because the probability of x being greater than or equal to 5 is equal to the width of the interval from 5 to 6 (which is 6-5 = 1) divided by the total length of the interval (which is 6-3 = 3).
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5. Simplify the expression. √80x²y • √25xy^4
Answers
Answer:
i think the answer is 20√5x^3y^5
Factor the GCF out of each term of the polynomial.
Answers
Answer For The Number 22: Factors of 22 are 1, 2, 11, 22. There are 4 integers that are factors of 22. The greatest factor of 22 is 22. 3.
Answer For The Problem 2x3 (Divide it by the numbers I give you meaning divide the number two by what I give yo and the other number 3 by it.
The common factors for 2,3 are −1,1 . The numbers do not contain any common variable factors. The GCF (HCF) of the numerical factors −1,1 is 1 .The number is one.
Answer For The Problem 2x5 is also 1 so decide both 2&5 by 1 then multiply. After doing that for answers 2&3 add them. last if you then subtract 22 that might be the answer so put that & also put the answer of the greatest common factor of 22 which is 3. Make sure to include that the one where you subtracted 3 was the greatest common factor for 22.
Below is the graph of a cosine function in the form y = acos(bx) Which statements are true? Check all that apply.
A) The graph is horizontally compressed by a factor of 1/2.
B) The period is 2pi
C) The frequency is 1/(2pi)
D) The graph is stretched vertically by a factor of 2.
E) The period is pi
Answers
Answer:
The graph is horizontally compressed by a factor of One-half
The graph is stretched vertically by a factor of 2.
The period is π.
Answer:
A D E
Hope this helps :D
Choose the expression equivalent to: (10 x 18) + (10 x s)
A) 20x18s AND 180 + 10s
B) 180 + 10s AND 10(18 + s)
C) 10(18 + s) AND 20 x 18s
Giving brainlest
Answers
B. 180 + 10s. AND 10(18 + s)
Hope this helps! :)
ricardo's recipe for 4 loaves of bread requires 6/7 of oil he only wants to make one loaf how much oil does he need for one loaf? PLEASE HELP IVE BEEN STUCK ON THIS FOR A HOUR!
Answers
Answer: ive had a question for many years and still no answered
Step-by-step explanation:
10. Write in slope-intercept form:
-3x + 4y = 12
Answers
Answer:
Step-by-step explanation:
Write in slope-intercept form:
-3x + 4y = 12 is
Slope = 1.500/2.000 = 0.750
x-intercept = 12/-3 = 4/-1 = -4.00000
y-intercept = 12/4 = 3
The midpoints of the sides of a triangle are shown. Graph the mid-segment triangle. Then graph the original triangle.
Answers
Given: the midpoints of the sides of a triangle are shown.
We will graph the mid-segment and the original triangle
The graph of the mid-segments are as shown in the given picture
To graph the original triangle, we will draw 3 parallel lines from the given points and each will be 2 times of the opposite side of the mid-segment
See the following figure:
As you can see, every two parallel lines with the same color
And each side is two times the mid-segment opposite to that side.
The graph with the mid-segment triangle is shown below.
What is the triangle?In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
It is given that, the midpoints of the sides of a triangle are shown.
The original triangle and the mid-segment will be graphed. The offered image depicts the graph of the mid-segments. We will create three parallel lines from the supplied locations that are each twice as long as the mid-opposite segment's side in order to graph the original triangle.
View the illustration below. As you can see, the mid-segment on the opposite side of every pair of parallel lines with the same color is twice as large.
Thus, the graph with the mid-segment triangle is shown below.
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Identify the slope of the line for the equation y= 1/6x + 1/4
Answers
Answer:
1/6x or just 1/6
Step-by-step explanation:
the equation is y = mx + b and 1/6x is in place m which is the slope
stream blueberry eyes by MAX AND SUGA periodTt
The slope is also known as the gradient and the rate of change of the line. The slope of the line for the equation y= 1/6x + 1/4 is 1/6
Slope of a lineThe slope is also known as the gradient and the rate of change of the line, The equation of aline in slope intercept form is expressed as:
y = mx + b
where
m is the slope
b is the y-intercept
Given the equation y = 1/6x + 1/4
Compare
mx = 1/6x
m = 1/6
Hence the slope of the line for the equation y= 1/6x + 1/4 is 1/6
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A farmer plants wheat and corn. It costs about $150 per acre to plant wheat and about $350 per acre to plant corn. The farmer plans to spend no more than $250,000 planting wheat and corn. The total area of corn and wheat that the farmer plans to plant is less than 1200 acres
Answers
The inequality that models this situation is 150x + 350 y ≤ 250000 and x + y < 1200
What is an inequality?
An inequality is an expression that shows the non equal comparison of two or more numbers and variables.
Let x represent the number of wheat acres and y represent the number of corn acres, hence:
150x + 350 y ≤ 250000 (1)
Also:
x + y < 1200 (2)
The inequality that models this situation is 150x + 350 y ≤ 250000 and x + y < 1200
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suppose that scores on a certain IQ test are normally distributed with mean 110 and standard deviation 15. then about 40% of the scores are between
Answers
Answer:
102 and 118
Step-by-step explanation:
Which expression is equivalent to the one that is modeled?
Answers
Answer:
What are the equivalent expressions?
Two expressions are said to be equivalent if they have the same value regardless of the value of the variable(s) in them.
Step-by-step explanation:
Jordan can ride her skateboard 75 meters in 30 seconds. How long will it take Jordan to ride her skateboard 1500 meters.
Answers
Step-by-step explanation:
1500÷75= 20
30×20= 600 seconds
600÷60= 10 minutes