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Emperical finance, full summary
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Emperical finance, full summary, VU (week 1 untill 6)
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Topics Mathematics (5 clips) Functions
Sigma notation
Differential calculus
Matrices
Topics Statistics (6 clips)
Random variables, events, pdf/cdf
Expected values, mean/(co)variance rules and correlations
Some important distributions
From population to a sample
Hypotheses testing/ p-values
Functions: Clip 1:
A linear function:
Interpretation of parameters: start at 25, 0,05 up for every hour studied
Root of the function, when is y equal to zero, negative amount for this. -25=0,05x,
solve.
Quadratic function: a positive, u shaped, a negative, n shaped.
A polynomial adds higher order powers of x into the function:
The roots of a quadratic function: a quadratic function has two roots:
Power of number of variables, 7 frequently used numbers: WRITE BEHIND
1
,Write down:
One example:
Write down:
2
,Clip 2: Functions part II: exponent and logarithmic
Exponential function:
It is sometimes the case that the relationship between two variables is best described
by an exponential function
- For example, when a variable grows (or reduces) at a rate in proportion
to its current value, we would write y = e^x with e a simple number:
2.71828.
Logarithms:
Logarithms were invented to simplify cumbersome calculations, since exponents can
then be added or subtracted, which is easier than multiplying or dividing the original
numbers
- Consider the power relationship 2^3 = 8
Using logarithms, we would write this as log2 8 = 3, or ‘the log to the base 2 of 8 is 3’
Hence, we could say that a logarithm is defined as the power to which the base must
be raised to obtain the given number More generally, if a^b = c, then we can also
write:
3
, The law of logs:
Example:
Write down:
4
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