Recall in class we showed the derivation of logistic regression from Naive Bayes as- sumptions. At that time, we assumed the variance o2 of class-conditional probability distri- bution is independent of class index k and feature index j. Now we generalize it by removing the assumption of ožk being independent of j and k. Namely, ok of the class-conditional probability distribution p(x;\y = k) now depend on both indices. jk - Is the new form of p(x;\y = k) still implying the same logistic regression formula p(y|X)? If not, write down the new form of logistic regression.
Answers
In the original derivation of logistic regression from Naive Bayes assumptions, we assumed that the variance σ^2 of a class-conditional probability distribution is independent of class index k and feature index j. Now, by generalizing and allowing σ^2_jk to depend on both indices, the class-conditional probability distribution p(x|y=k) is now affected by this change.
This new assumption affects the logistic regression formula p(y|X) because it no longer relies on the original independence assumption. Consequently, the logistic regression model will need to account for the new variances σ^2_jk, which depend on both class index k and feature index j.
The new form of logistic regression will likely be different from the original formula, as it must now accommodate the modified variances in class-conditional probability distributions. Unfortunately, without more information, it is not possible to provide the exact new form of logistic regression here. However, it's important to note that this new form should consider the dependency of σ^2_jk on both indices j and k.
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Related Questions
Does anyone know the area?
Answers
Answer:
69
Step-by-step explanation:
4x3=12
9x5=45
2x6=12
45+12+12=69
Need help on this, I have no idea what should go on the first line or the second line
Answers
Answer:
1.) 120
2.)120
Step-by-step explanation:
1.) Do length times width
2.) For the number 120 you don't have to round, so it just stays the same
sales for the dress department last year were $82,000. the manager for the department plans an increase of 12.5or this year. what is this year's projected sales volume?
Answers
Sales for the dress department last year were $82,000. The manager for the department plans an increase of 12.5% this year. So, the projected sales volume for this year is $92,250.
To calculate this year's projected sales volume we will add 12.5% of the sales of the last year to the sales of last year. This can be calculated by using the formula:
S = P + (P × r / 100)
Where S is new sales, P is old sales, and r is a rate of increase.
In this problem, the value of P is $82,000 and the rate of increase is 12.5%. Now, let's plug these values into the formula and solve for S:
S = P + (P × r / 100)
S = $82,000 + ($82,000 × 12.5 / 100)
S = $82,000 + $10,250S = $92,250
Hence, the projected sales volume for this year is $92,250.
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John sections a circular garden with a 12-yard diameter into qual sections. He wants to put a border around one section of the garden To tenth what is the perimeter one section of the garden 4. 7 yards 14. 1 yards 16. 7 yards 377 yards
Answers
John sections a circular garden with a 12-yard diameter into equal sections. He wants to put a border around one section of the garden. To tenths, what is the perimeter of one section of the garden.
Given, Diameter of circular garden = 12 yardsRadius of garden = diameter/2 = 12/2 = 6 yardsArea of circular garden = πr² = π × 6² = 36π sq.yardsIf the circular garden is divided into ‘n’ equal parts, then the area of each part will be:Area of one part = (Area of the garden)/n= (36π)/n sq.yardsSince each part is circular in shape, its circumference will be the perimeter of that part:Circumference of one part = 2πr/n = (2π/ n) × 6= (12π/n) yardsSince the circumference has to be in tenths, we need to round off the value of (12π/n) to the nearest tenth. Here, we are rounding off to one decimal place:
Round off (12π/n) to one decimal place = 1.9nCircumference of one part = 1.9n yardsAccording to the question, we have to find the value of circumference of one part. So, we need to find the value of ‘n’.To find the value of ‘n’, we need to make use of the information given in the question.
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Given that f(x) = x2 + 9x + 20 and g(x) = x + 5, find f(x) + g(x) and
express the result in standard form.
Answers
Answer: x² + 10x +25
Step-by-step explanation:
f(x) + g(x) = x² +9x +20 + x + 5 = x² + 10x +25
Answer:x^2+8x+16
Step-by-step explanation:
If there are 12 quarters, find the total number of coins in Lucy's coin collection.
Answers
Answer:
300
Step-by-step explanation:
a quarter is worth 25 cents then do 12 times 25 witch is 300
As the department manager, you've just been informed the organization is having to cut back on expenses This means some departments likely will incur employee losses. You are to attend a managers meeting to justify your department's current budget. The best chart to show how your department's expenses compare to the total company's expenses, and hopefully save employee jobs, would be: column chart line chart bar chart pie chart
Answers
Answer:
The best chart to show how your department's expenses compare to the total company's expenses, and hopefully save employee jobs, would be:
Pie Chart
Step-by-step explanation:
PLS CAN SOMEONE HELP ME PLS
Answers
Answer:
20 m
Step-by-step explanation:
Let the length of the perpendicular dropped from vertex C to segment AB be x
By geometric mean property:
\(x = \sqrt{16 \times 9} \\ \\ x = \sqrt{144} \\ \\ x = 12 \: m \\ \\ By \: Pythagoras \: Theorem: \\ \\ Distance \: across \: the \: pond \\ \\ = \sqrt{ {16}^{2} + {12}^{2} } \\ \\ = \sqrt{256 + 144} \\ \\ = \sqrt{400} \\ \\ = 20 \: m\)
In some languages, every consonant must be followed by a vowel. How many seven-letter ‟words” can be made from the Hawaiian word MAKAALA if each consonant must be followed by a vowel?
Answers
Answer:
One. Kamala.
Step-by-step explanation:
What is the slope of the line in this graph?
Answers
Answer:
The slope of the line is 7/5.
Step-by-step explanation:
To find the slope, first, find two points. On this line, two points are 0,0 and 7,5. Using the slope formula, we get 7-0/5-0. This gives 7/5, and that's the slope.
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Given 0 ≤ θ < 2π , solve 2 csc x = 3 csc θ − csc θ sin θ .
Answers
The solution to the equation 2 csc x = 3 csc θ − csc θ sin θ in the range 0 ≤ θ < 2π is:
θ = 7π/6
We can start by manipulating the given equation to express cscθ in terms of cscx:
2 csc x = 3 csc θ − csc θ sin θ
2/cscθ = 3 - sinθ
cscθ/2 = 1/(3 - sinθ)
cscθ = 2/(3 - sinθ)
Now we can use the identity sin²θ + cos²θ = 1 and substitute for cscθ in terms of sinθ:
1/cosθ = 2/(3 - sinθ)
cosθ = (3 - sinθ)/2
Next, we can use the identity sin²θ + cos²θ = 1 to solve for sinθ:
sin²θ + cos²θ = 1
sin²θ + [(3 - sinθ)/2]² = 1
Multiplying both sides by 4, we get:
4sin²θ + (3 - sinθ)² = 4
Expanding and simplifying, we get:
8sin²θ - 6sinθ - 8 = 0
Dividing both sides by 2, we get:
4sin²θ - 3sinθ - 4 = 0
Using the quadratic formula with a = 4, b = -3, and c = -4, we get:
sinθ = [3 ± √(3² - 4(4)(-4))]/(2(4))
sinθ = [3 ± √49]/8
sinθ = (3 ± 7)/8
Since 0 ≤ θ < 2π, we only need to consider the solution sinθ = (3 - 7)/8
= -1/2 corresponds to an angle of 7π/6 in the third quadrant.
To find cosθ, we can use the identity sin²θ + cos²θ = 1:
cosθ = ±√(1 - sin²θ)
Since we are in the third quadrant, we want the value of cosθ to be negative, so we take the negative square root:
cosθ = -√(1 - (-1/2)²)
cosθ = -√(3/4)
cosθ = -√3/2
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if jack is at the store and can buy any three fruits (the store sells apples, oranges, pears, bananas, plums, grapefruit and kiwis), how many combinations of fruit can he choose?
Answers
Jack has a total of 35 different combinations of fruits to choose from at the store.
To calculate the number of combinations Jack can choose, we need to use the concept of combinations in mathematics. Since Jack can buy any three fruits out of the seven available options, we need to calculate the number of combinations of 7 fruits taken 3 at a time.
The formula to calculate combinations is C(n, r) = n! / (r! * (n - r)!), where n is the total number of options and r is the number of options to be chosen.
In this case, n = 7 (total number of fruits) and r = 3 (fruits to be chosen). Plugging these values into the formula, we get:
C(7, 3) = 7! / (3! * (7 - 3)!)
= (7 * 6 * 5 * 4!) / (3 * 2 * 1 * 4!)
= (7 * 6 * 5) / (3 * 2 * 1)
= 35
Jack has a total of 35 different combinations of fruits to choose from at the store. He can select any three fruits out of the available options, which include apples, oranges, pears, bananas, plums, grapefruit, and kiwis.
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Keshav gave Rs. 3298.36 to his brother and Rs. 2149.67 to his sister. The remaining amount was given to his mother. If he had Rs. 9764.32 in all, how much did he give to her mother. ?
Answers
If x=3 and y=7, evaluate the following expression: 20+2(3y−4x)
Answers
=20+2(3(7)-4(3))
=20+2(21-12)
=20+2(9)
=20+18
=38
Given
x = 3, y = 7
To find out:
The value of 20 + 2(3y - 4x)
Solution:
20 + 2(3y - 4x)Let us put the value of x and y as given.
= 20 + 2 (3 × 7 - 4 × 3)Now, solve the bracket portion. First do the multiplication.
= 20 + 2 (21 - 12)Now, subtract.
= 20 + 2 (9)Multiply 9 with 2.
= 20 + 18Finally, add the two.
= 38Answer:
38
Hope you could understand.
If you have any query, feel free to ask.
Prove by induction: 2+8+14+...+(6n - 4) = n(3n - 1)
Answers
We have proved by induction that 2 + 8 + 14 + ... + (6n - 4) = n(3n - 1) for all positive integers n.
We have,
To prove the statement by induction, we will follow the standard steps of an induction proof:
Base case:
We first show that the statement holds for n = 1.
When n = 1, the left-hand side of the equation becomes 2, and the right-hand side becomes 1(3 - 1) = 2.
Since both sides are equal, the statement holds for n = 1.
Inductive step:
We assume that the statement holds for some arbitrary positive integer k and then prove that it holds for k + 1.
Inductive hypothesis:
Assume that the equation holds for k, i.e., 2 + 8 + 14 + ... + (6k - 4)
= k(3k - 1).
We need to prove that the equation also holds for k + 1, i.e., 2 + 8 + 14 + ... + (6(k + 1) - 4) = (k + 1)(3(k + 1) - 1).
Starting from the left-hand side of the equation for k + 1:
2 + 8 + 14 + ... + (6(k + 1) - 4)
We can rewrite this as:
(2 + 8 + 14 + ... + (6k - 4)) + (6(k + 1) - 4)
Using the inductive hypothesis, we can substitute the expression for k:
k(3k - 1) + (6(k + 1) - 4)
Simplifying further:
3k² - k + 6k + 6 - 4
3k² + 5k + 2
Now, let's simplify the right-hand side of the equation for k + 1:
(k + 1)(3(k + 1) - 1)
(k + 1)(3k + 3 - 1)
(k + 1)(3k + 2)
Expanding the expression:
3k² + 2k + 3k + 2
Combining like terms:
3k² + 5k + 2
As we can see, the left-hand side of the equation for k + 1 is equal to the right-hand side of the equation for k + 1.
Conclusion:
Since we have proven that the statement holds for n = 1 (base case) and have shown that if it holds for some k, it also holds for k + 1 (inductive step), we can conclude that the statement holds for all positive integers n by the principle of mathematical induction.
Therefore,
We have proved by induction that 2 + 8 + 14 + ... + (6n - 4) = n(3n - 1) for all positive integers n.
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3(2x) + 4y(5)
what is the equivalent fraction
hurry please .
Answers
Answer:
6+20y
y=_14
Step-by-step explanation:
6+20y
y=_14
Which represents the solution(s) of the graphed system of equations, y = –x2 + x + 2 and y = –x + 3?
(1, 2)
(1, 2) and (0, 3)
(–1, 0) and (2, 0)
(2, 1)Which represents the solution(s) of the graphed system of equations, y = –x2 + x + 2 and y = –x + 3?
(1, 2)
(1, 2) and (0, 3)
(–1, 0) and (2, 0)
(2, 1)
Answers
The solution(s) of the graphed system of equations are approximately (2.82, 1.66) and (-0.82, 3.82).
To find the solution(s) of the graphed system of equations y = -x² + x + 2 and y = -x + 3, we need to determine the point(s) where the two equations intersect on the graph.
By setting the two equations equal to each other, we can find the x-coordinate(s) of the intersection point(s):
-x² + x + 2 = -x + 3
Simplifying the equation, we get:
-x² + x + x - 2 = 3
Combining like terms, we have:
-x² + 2x - 2 = 3
Rearranging the equation, we get:
-x² + 2x - 2 - 3 = 0
Simplifying further, we have:
-x² + 2x - 5 = 0
To solve this quadratic equation, we can either factor it, complete the square, or use the quadratic formula. Upon solving, we find that the equation has two real solutions: x ≈ 2.82 and x ≈ -0.82.
Substituting these values back into either of the original equations, we can find the corresponding y-coordinates. For example, using the equation y = -x² + x + 2:
For x ≈ 2.82, y ≈ -2.82² + 2.82 + 2 ≈ 1.66
For x ≈ -0.82, y ≈ -(-0.82) + 3 ≈ 3.82
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The complete question:
What are the solutions of the graphed system of equations, y = –x² + x + 2 and y = –x + 3?
The radius of a circle is 13m. Find it’s area in terms of pi
Answers
Answer:
169pi
Step-by-step explanation:
Area of a circle: \(\pi\)r²
pi × 13 × 13= 169pi
Answer: 169ip
Step-by-step explanation:
Tyee was driving down a road and after 2 hours he had traveled 54 miles. At this speed, how many miles could Tyee travel in 8 hours?
Answers
The number of miles that Tyee will travel in 8 hours, given the speed is 216 miles
How to find the miles driven ?To find the number of miles that Tyree would drive in 8 hours, given the speed he is going, you first need to find the speed Tyree is going which is:
= Number of miles travelled / Number of hours
= 54 / 2
= 27 miles per hour
The number of miles that Tyree would travel in 8 hours is:
= Number of hours of travelling x Speed travelled
= 8 x 27
= 216 miles
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can Someone Answer This Please! The Question Is on the Attached Photograph Below: Thanks!
Answers
Answer:
a^5÷a^3=a^5×a^-3=a^5+-3=a^2
Answer:
\(a) \: \: {a}^{2} \)
\(b) \: \: c\)
Step-by-step explanation:
\(a) \: \: {a}^{5} \div {a}^{3} \\ = (a \times a \times a \times a \times a)(a \times a \times a) \\ = a \times a \\ = {a}^{2} \)
\(b) \: \: \frac{ {c}^{4} }{ {c}^{3} } \\ \frac{(c \times c \times c \times c)}{(c \times c \times c)} \\ = c\)
Hope it is helpful.....Cyrus' tennis match lasted two and a half hours. Everett's tennis match lasted four and a half hours. How much longer did Everett’s match last?
Answers
Answer:
2 hours
Step-by-step explanation:
4.5 - 2.5 = 2
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Let us suppose the following profit function for this industry: π(p,w
1
,w
2
)=
8(w
1
+w
2
)
1/2
p
2
where p is the market price of its output, while w
1
and w
2
are the prices of the inputs. Assume further that the firms are identical and that each firm faces the same market prices for both its output as well as inputs. a) Explain whether the firm is operating in the short run or long run and further determine the supply function for each firm. b) Derive the firm's input demand functions, determine their degree of homogeneity as well as the impact of a change in the input prices. c) Derive the market supply function given that there are 40 firms operating in this, market. d) If the market price of output (p) is 5 , the market price of the input (w
1
) is 1 , that of (w
2
) is also 1 and the demand function is given by q=1500/p(p+1). Determine the total market supply.
Answers
(a) The firm is operating in the long run, and its supply function is determined by the profit maximization condition.
(b) The firm's input demand functions can be derived from the profit function, and their degree of homogeneity is 1/2. Changes in input prices will impact the firm's input demand.
(c) The market supply function can be derived by aggregating the supply functions of all 40 firms operating in the market.
(d) Given the market conditions and demand function, the total market supply can be calculated.
(a) The firm is operating in the long run because it has the flexibility to adjust its inputs and make decisions based on market conditions. The firm's supply function is determined by maximizing its profit, which is achieved by setting the marginal cost equal to the market price. In this case, the supply function for each firm can be derived by taking the derivative of the profit function with respect to the price of output (p).
(b) The input demand functions for the firm can be derived by maximizing the profit function with respect to each input price. The degree of homogeneity of the input demand functions can be determined by examining the exponents of the input prices. In this case, the degree of homogeneity is 1/2. Changes in the input prices will affect the firm's input demand as it adjusts its input quantities to maximize profit.
(c) The market supply function can be derived by aggregating the individual supply functions of all firms in the market. Since there are 40 identical firms, the market supply function can be obtained by multiplying the supply function of a single firm by the total number of firms (40).
(d) To determine the total market supply, we substitute the given market conditions and demand function into the market supply function. By solving for the market quantity at a given market price, we can calculate the total market supply.
In conclusion, the firm is operating in the long run, and its supply function is determined by profit maximization. The input demand functions have a degree of homogeneity of 1/2, and changes in input prices impact the firm's input demand. The market supply function is derived by aggregating the individual firm supply functions, and the total market supply can be calculated using the given market conditions and demand function.
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If pH = -log [H+], find the pH of a substance that has a hydrogen concentration [H+] = 5.7 X 10-4.Round your answer to the nearest ten thousandth (4 decimals).
Answers
[H+] = -1.7243
Explanation:
Since [H+] = 5.7 * 10 - 4, in the function -log[H+] representing pH, replace H+
pH = -log [5.7 *10 - 4]
pH = -log[53]
pH = -1.7243
NB:
This number is rounded up from -1.72427.....
7 less than twice a number is greater than 19
Answers
Answer:
Step-by-step explanation:
if the number is x
2x - 7 greater than 19
= 2x greater than 26
Find the first three nonzero terms of the Maclaurin series for the function and the values of x for which the series converges absolutely f(x)=(2 sin x) In (1 + x) What are the first three nonzero terms of the Maclaurin series for f(x)?
Answers
The first three nonzero terms of the Maclaurin series for the function f(x) = (2 sin x) ln(1 + x) are: 2x - (2/3)x^3 + (4/45)x^5. The Maclaurin series converges absolutely for all values of x within the interval -1 < x ≤ 1.
To find the Maclaurin series for f(x), we need to express the function as a power series centered at x = 0. We can do this by using the known Maclaurin series expansions for sin x and ln(1 + x).
The Maclaurin series expansion for sin x is:
sin x = x - (1/3!)x^3 + (1/5!)x^5 - ...
The Maclaurin series expansion for ln(1 + x) is:
ln(1 + x) = x - (1/2)x^2 + (1/3)x^3 - ...
Multiplying these two series, we obtain the Maclaurin series expansion for f(x):
f(x) = (2 sin x) ln(1 + x) = 2x^2 - (2/3)x^3 + (4/45)x^5 - ...
The first three nonzero terms of the Maclaurin series for f(x) are: 2x - (2/3)x^3 + (4/45)x^5.
To determine the values of x for which the series converges absolutely, we need to consider the interval of convergence. In this case, the Maclaurin series converges absolutely for all values of x within the interval -1 < x ≤ 1.
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if there are 60 songs on a mp3 and 21 are rock. what is the ration of rock songs not being played at all
Answers
Answer:
rock: not rock
7:13
Step-by-step explanation:
First determine how many songs are not rock
60-21 = 39
There are 39 songs that are not rock
ratio of rock to not rock
rock: not rock
21:39
We can divide by 3
21/3:39/3
7 : 13
how many times as many robberies were there actually in year 4 compared to year 2? round your answer to 2 decimal places.
Answers
The number of robberies in year 4 is 1.14 times the number of robberies in year 2.
the number of robberies in the year 4 is 255.
the number of robberies in year 2 is 225.
Now to find how many times the robberies took place in year 4 than in year 2 we will take the ratio as follows-
number of robberies in year 4/number of robberies in year 2 = 255/225
hence, we have,
number of robberies in year 4/number of robberies in year 2 = 17/15
number of robberies in year 4/number of robberies in year 2 = 1.13333
number of robberies in year 4/number of robberies in year 2 = 1.14
or we can say that number of robberies in year 4 = 1.14 * the number of robberies in year 2
i.e number of robberies in year 4 = 1.14 times the number of robberies in year 2.
Hence, the number of robberies in year 4 is 1.14 times the number of robberies in year 2.
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The complete question is -
how many times as many robberies were there actually in year 4 compared to year 2? round your answer to 2 decimal places.
According to a poll, 56% of voters support funding a new community center. a surveyor randomly selects 75 voters and asks each voter if he or she is in favor of the center. if being in favor of the center is a success, what is the probability of a success for this binomial experiment?
Answers
The probability of a success for this binomial experiment is 0.56.
What is the probability of a success?
Probability is used to determine how likely it is that a stated event would occur. The probability usually lies between 0 and 1.
A binomial experiment is an experiment where there is a fixed number of trials, and the results are usually between two options- a success or a failure.
The probability of a success = 56 / 100 = 0.56
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Consider this set of numbers: 1, 1, 2, 2, 3, 3, 4, 7, 7, 7, 8, 9. the _____ of the set is 7.
Answers
Answer:
mode
Step-by-step explanation:
The mode of the set is 7, as 7 is the number that occurs the most frequently.
A solution containing 30% juice is mixed with a solution containing 10% juice to make 100 gallons of solution that makes 12% juice.How much of the 30% solution was used
Answers
Let the amount of the 30% solution be x gallons.
Then the amount of the 10% solution is (100 - x) gallons.
The amount of juice in the 30% solution is 0.3x gallons.
The amount of juice in the 10% solution is 0.1(100 - x) gallons.
When the two solutions are mixed, we get 100 gallons of a 12% juice solution, which means:
0.3x + 0.1(100 - x) = 0.12(100)
Simplifying this equation, we get:
0.3x + 10 - 0.1x = 12
0.2x = 2
x = 10
Therefore, 10 gallons of the 30% solution was used.
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