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a group of equal proportions - the definition of quantile is one of a class of values of a variate that divides the total frequency of a sample or population into a given number of equal proportions

1 answer



Yes.

Usually the value of the lower quantile, median, and upper quantile are in ascending order, how if for the particular set of data, if all values are the same, then these three measures can be the same.

1 answer


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Victor Chernozhukov has written:

'Quantile regression with censoring and endogeneity'

'An IV model of quantile treatment effects' -- subject(s): Accessible book

'Rearranging Edgeworth-Cornish-Fisher expansions'

'L1-Penalized Quantile Regression in High Dimensional Sparse Models' -- subject(s): Regression analysis

'Instrumental variable quantile regression' -- subject(s): Accessible book

'Extremal quantities and value-at-risk' -- subject(s): Accessible book

'Estimation and confidence regions for parameter sets in econometric models' -- subject(s): Accessible book

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Quantile regression is considered a natural extension of ordinary least squares. Instead of estimating the mean of the regressand for a given set of regressors, and instead of minimizing sum of squares, it estimates different values of the regressand across its distribution, and minimizes instead the absolute distances between observations.

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Lingxin Hao has written:

'Quantile regression' -- subject(s): Statistical methods, Regression analysis, Social sciences

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The interquartile range is well known as a measure of statistical dispersion. It is equal to difference between upper and lower quartiles. The quartiles is a type of quantile.

1 answer


According to SOWPODS (the combination of Scrabble dictionaries used around the world) there are 1 words with the pattern Q-AN--L-. That is, eight letter words with 1st letter Q and 3rd letter A and 4th letter N and 7th letter L. In alphabetical order, they are:

quantile

1 answer


Qinglai Meng has written books in the field of Statistics, particularly focusing on mixed effects models, quantile regression, and other statistical methodologies. He has also published research articles in various statistical journals.

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In astrology, a sextile is an aspect that occurs when two planets are approximately 60 degrees apart. It is considered a harmonious aspect that can create opportunities for growth and cooperation between the planets involved.

2 answers


If the exponential distributions have the same scale parameter it's known as the Erlang-2 distribution. PDF and CDF exist in closed-form but the quantile function does not.

If you're looking to generate random variates the easiest method is to sum exponentially distributed variates. If the scale parameter is the same you can simplify a bit: -log(U0) - log(U1) = -log(U0*U1).

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Doryun Sok is an author known for writing about contemporary Korean art and modern art history. His work often focuses on Korean artists and their impact on the global art scene. Sok's writings provide insights into cultural exchanges and the development of art in Korea.

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1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 +

3 answers


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2 answers




10 x 10=100. Would you rather go like this: 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=100?

12 answers



1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 5

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10

1 1 1 1 1 1 1 1 1 1 5 5 5

1 1 1 1 1 1 1 1 1 1 5 10

1 1 1 1 1 5 5 5 5

1 1 1 1 1 5 5 10

1 1 1 1 1 10 10

5 5 5 5 5

5 5 5 10

5 10 10

12 ways

2 answers



I assume by "square numbers" you mean perfect squares.

You didn't say how many of each were allowed:

1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1²= 23

1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² = 23

1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² + 2² = 23

1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 3² = 23

1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² + 2² + 2² = 23

1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² + 3² = 23

1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² + 2² + 2² + 2² = 23

1² + 1² + 1² + 1² + 1² + 1² + 1² + 4² = 23

1² + 1² + 1² + 1² + 1² + 3² + 3² = 23

1² + 1² + 1² + 2² + 2² + 2² + 2² + 2²= 23

1² + 1² + 1² + 2² + 4² = 23

1 answer


1+1+1+1+1+1+1+1+1+-1+1+1+10

1+1+1+1+1+1+1+1+1=9

1+1+1+1+1+1+1+1+1+-1=8

1+1+1+1+1+1+1+1+1+-1+1+1+10=20

1 answer



1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1

and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1

and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1

and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1

and 1 and 1 and 1 and 1 and 1 and 1.

Or

1.1 and 1.1 and 1.1 and 42.7

or an infinite number of other possibilities.

2 answers


(-1)3 = (-1)(-1)(-1) = -1

(-1)3 = (-1)(-1)(-1) = -1

(-1)3 = (-1)(-1)(-1) = -1

(-1)3 = (-1)(-1)(-1) = -1

3 answers


11111 x 11111 = 123454321

1 1 1 1 1

x 1 1 1 1 1

_______________

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

+ 1 1 1 1 1

_______________

1 2 3 4 5 4 3 2 1

1 answer


[Legend: Each number represents the denomination (amount) of the coin.]

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1 = 25

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+5 = 25

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+5+5 = 25

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+10 = 25

1+1+1+1+1+1+1+1+1+1+5+5+5 = 25

1+1+1+1+1+5+5+10 = 25

1+1+1+1+1+5+5+5+5 = 25

1+1+1+1+1+10+10 = 25

5+5+5+5+5 = 25

5+5+5+10 = 25

5+10+10 = 25

So the answer is 11!!!

I think you're missing 1+1+1+1+1+1+1+1+1+1+5+10 = 25 ?

1 answer



1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1 is one example.

1 answer


The answer is -1.

(1 + 1 x 1)/(1 - 1 x 1 -1) + 1 =

Follow the order of operations: parentheses/brackets, exponents, multiplication and division from left to right, and addition and subtraction from left to right.

Numerator:

Simplify 1 x 1 to 1.

(1 + 1)/(1 - 1 x 1 -1) + 1

Simplify 1 + 1 to 2.

2/(1 - 1 x 1 - 1) + 1

Denominator:

Simplify 1 x 1 to 1.

2/(1 - 1 - 1) + 1

Simplify 1 - 1 - 1 to -1.

2/(-1) +1

Simplify 2/(-1) to -2.

-2 +1

Simplify.

-1

4 answers


There are infinitely many possible solutions. One of them is

1 + 1 + 1 + 1 + 1 + 1 +1 + 1 + 1 + 1 +

1 + 1 + 1 + 1 + 1 + 1 +1 + 1 + 1 + 1 +

1 + 1 + 1 + 1 + 12

1 answer



1+1 is 2 and 1-1 is 0 and 1*1 is 1 and 1/1 is 1

1 answer



One possibility:

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1

1 answer


1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1 x 0

1 answer


1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1x0=

1 answer


They are -1 and +1.

They are -1 and +1.

They are -1 and +1.

They are -1 and +1.

2 answers


1 quarter, 2 dimes, 2 nickels, and 45 pennies

1+2+2+45=50

25+10+10+5+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=100

1 answer


1 quarter, 2 dimes, 2 nickels, and 45 pennies.

1+2+2+45=50

25+10+10+5+5+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1

1 answer


The reciprocal of 1 is 1.

Proof:

a. 1*(1/1) = 1 because a*(1/a) = 1

b. 1*1 =1 because 1*a = a

c. 1/1 = 1 compare a. and b.

7 answers


1+1-1+1-1+1-1+1-1+1-1+1-1+1-1*0+2

1 answer


1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 = 19

2 answers


1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 12 1 11 1 1 1

3 answers


There are infinitely many possible answers.

One such is 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+16

1 answer



It is negative infinity.

4 answers


There are no two numbers that multiply to get 6 but add to get 18. In fact, the solutions are:

  • 1x1x1x1x1x1x1x1x1x1x1x1x6 = 6; 1+1+1+1+1+1+1+1+1+1+1+1+6 = 18
  • 1x1x1x1x1x1x1x1x1x1x1x1x1x2x3 = 6; 1+1+1+1+1+1+1+1+1+1+1+1+1+2+3 = 18

1 answer