Working with Probabilities Physics 115a (Slideshow 1) A. Albrecht

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Working with Probabilities Physics 115a (Slideshow 1) A. Albrecht These slides related to Griffiths section 1.3. Consider the following group of people in a room:. Histogram Form. Consider the following group of people in a room:. Total people = 14.

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Working with Probabilities

Physics 115a (Slideshow 1)

A. Albrecht

These slides related to Griffiths section 1.3

Total people = 14

Total people = 14

Total people = 14

Assuming no age constraint, what is the probability of finding each age?

Related to collapse of the waveunction (“changing the question”)

Total people = 14

Related to collapse of the waveunction (“changing the question”)

Total people = 14

Lessons so far

• A simple application of probabilities
• Normalization
• “Re-Normalization” to answer a different question
• All of the above are straightforward applications of intuition.

Median = 23

Average = 21

Median = 23

Average = 21

Lesson: Lots of different types of questions (some quite similar) with different answers. Details depend on the full probability distribution.

Average (mean):

• Standard QM notation
• Called “expectation value”
• NB in general (including the above) the “expectation value” need not even be possible outcome.

Careful: In general

In general, the average (or expectation value) of some function f(j) is

Continuous Variables

Why not measure age in weeks?

The ages of students taking health in the 8th grade in a large school district (3000 students).