Math VS Computer
There is a star. From next year (year 1)
the star explosion probablity is 1%, after that, every year will
increase 1%
( 2nd year is 2%, 3rd year is 3%, 4th year is 4% ...)
Which year is the highest probablity to explosion?
Year 100? 100%? No!~~~
P(100)=99%*98%*97%......1%*100%
P(n)=99%*98%*97%......[100-(n-1)]%*n%=99*98*97...(100-n+1)*n/(100^n)
derivative of n! ?
P(n+1)/P(n)=(100-n)(n+1)/(100*n)
try to find when >1
N=9
which means P(10)/P(9)>1, and P(11)/p(10)<1
So, 10th year is the answer
P=6.28%
How many steps for Fib number?
1.618^n
Solve Linear Regression
Am I dying ?:
- There is a rare deadly disease is present in the population at 1 in 100,000
- A test for this disease will report positive for 99.5% of people with disease, and negative 99.9% of time for those without.
- One day, I took this test, and got a Postivite result. Am I dying?