# Mathematical and Computational Methods in Physics and Engineering (fall 2016)

## Daily outline for Fri, Sep 9, 2016 9:10 AM (10 months ago)

### Probability 2

assigned today:

Due today:
• probability of rolling a 2, then an even number, then a prime number.
• probability that a line is the best fit
• Math of maximum likelyhood for straight line

$$\sigma_x^2 =\frac{1}{N}\sum(x_i-\bar{x}_i)^2$$

$$x_i-\bar{x}_i\approx (u_i-\bar{u})\left(\frac{\partial x}{\partial u}\right)+(v_i-\bar{v})\left(\frac{\partial x}{\partial v}\right)$$

# what we did in class

First we did the quiz (birthday problem). Then we talked about how to help each other outside of class. We decided to try a google hangout this coming Sunday at 8 and maybe continuing to do them on Sundays, Tuesdays, and Thursdays (the night before each quiz).

I laid out the three problems, explaining the gist of them so that they could vote on what they wanted to spend class time on. They decided on the linear curve fitting.

I asked them to plot their best fit to 3 points and to indicate what was motivating them. Most of them said "try to get as close to the points as possible."

Then, to make sure they had a grip on the notion of multiplying probabilities, I asked them to comment on the dice problem above. I wasn't sure people could do it but they all did. Then we had a conversation about 1/2 vs 3/6 and 2,3, and 5 as ways to talk about the events. Very interesting.

Then we talked about what missing a point with a line meant from a probability perspective. We wrote down the product probability and talked about how it was a function of m and b (slope and y-intercept) and we talked about maximizing it. We discussed how that's related to minimizing the exponent (without the negative sign). Then I did one derivative for them and we talked about how you really just get 2 linear equations with m and b as the unknowns. We didn't have time to talk about the errors on the estimates and I just decided to drop that.

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