- Math colloquium
- Thursday, Oct. 30, 2:30 PM
- Newton 202
- Paul Wenger, RIT
- “Unique Saturation and Eigenvalue Methods for Graphs”
- Extra credit for going and writing summary
- What should second part of integration lab look like?
- Summary
- Bernoulli trial: success vs failure
- For example, flipping a coin to see if you get heads
- Bag-of-marbles problem, try to draw red marble, as long as you replace marbles after drawing
- Success probability is always p, failure is 1-p
- Calculate first time success occurs
- First success is after n-1 failures, so probability of taking n trials to get first success is p(1-p)n-1
- Expected number of trials ’til 1st success = 1/p
- Bernoulli trial: success vs failure
- Experiment
- Try flipping a coin until it produces heads
- Count how many flips it took to get the “success”
- Repeat this process many times
- Results tabulated and graphed with Matlab
>> c=[] c = [] >> c(1) = 47 c = 47 >> c(2) = 29; >> c(3)= 8; >> c(4) = 2; >> c(5) = 1; >> c(6) = 1; >> c(7) = 1; >> c c = 47 29 8 2 1 1 1 % c(i) = # experiments that took i trials >> plot( c ) >> sum(c) % Total number of experiments we did ans = 89
- Algorithm for doing a Matlab simulation of this experiment
- (Presumably with a much larger number of series of flips/rolls)
Decide what is “success” Repeat many times: Do until success: Flip coin
- (Presumably with a much larger number of series of flips/rolls)
- While loops
- Read section 5.3