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Playing card probability
hence,
p = n/S =(4*13*13*13*36!/(10!*26!))/(52!/(13!*39!))
=> p = 4*13*13*13*36!*13!*39!/(52!*10!*26!)
=> p = 4*13*13*13*36!*13*12*11*39!/(52!*26!)
[because, 13!/10! = 13*12*11]
=> p = 4*13*13*13*36!*13*2*11*39!/(52!
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Important information about logistic models
into
1/13*p + 1/(13)(13-p) which makes our differential equation
dp dp
---- + --------- = (2/1300) * dt
13*p 13*(13-p)
Integrating we get:
(1/13)*ln(p) - (1/13)*ln(13-p) = (2/1300) * t + c
(1/13)*(ln(p)-ln(13-p) = (2/1300)*
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Predicting Exchange Rates
Note: Y- refers to the exchange rate of the Chinese Yuan to US Dollar
Date Period Chinese Yuan to US dollar
2-Jan-13 13 0.159000
1-Feb-13 14 0.159000
1-Mar-13 15 0.159000
2-Apr-13 16 0.159000
1-May-13 17 0.159000
1-Jun-13 18
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Completing the square: Finding the vertex and intercepts - repel, attract or are indifferent?
f(x)=x^2+13/3x+7/3
=x^2+2*(13/6)x+(13/6)^2-(13/6)^2+7/3
=(x+13/6)^2-169/36+7/3
=(x+13/6)^2-169/36+84/36
=(x+13/6)^2-85/36
Vertex: Notice that if we take x^2, shift it to the left by 13/6
and then shift it down by 85/36, we get f(x).
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Pert network diagram
13 10
7 G no 4 3 7 9 13 6
8 H no 4 5 9 12 16 7
9 I Yes 8 5 13 5 13 0
10 J no 2 13 15 14 16 1
11 K Yes 0 13 13 13 13 0
12 L Yes 3 13 16 13 16 0
Project Completion Time = 16 weeks
Number of Critical Path(s) = 1
The critical Path is A-D-I-K-L
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Estimating the price of a bond
13%)^13)+1000/(1+13%)^13
=$755.13.
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SSE/Sum of Squares for Error Calculations
.+ (10-8)² + (11-13)² + (12-13)² +...+ (15-13)² = 20. First, why do you get 18? because you are calculating SSE = (6-8)² + (7-8)² + (10-8)² + (11-13)² + (12-13)² + (15-13)² =18
Then, "..." means "some expression is omitted due to line space".
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Variance Testing : Analysis-of-variance Test
, 10, 13, 16, 17, 12, 11, 17
c. 15, 13, 13, 14, 15, 20, 15, 14, 9, 16, 12
d. 16, 12, 13, 12, 14, 11, 8, 13, 17, 15, 14
Please see the attached file for the complete solution.
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Magic Square
The sum of the numbers in each row, column, and diagonal should be 39.
3x3 magic square = [13 13 13
13 13 13
13 13 13]
When we add row, column and diagonal
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NMR Spectrum and 13C Label
The formation of [n-(13)C]-Glu, [n-(13)C]-Gln (n = 2 or 3), [2-(13)C]-aspartate
(Asp), [3-(13)C]-Asp, [3-(13)C]-alanine (Ala), and [3-(13)C]-lactate (Lac) was also
observed to be reproducible.