Homework Set # 4 - Due September 22

1. Consider the velocity of a gas particle in one dimension (-∞<v<∞).

a) Find the unbiased probability density p_1(v), subject only to the constraint that the average speed is c, that is, <|v|>=c.

b) Now find the probability density p_2(v), given only the constraint of the average kinetic energy, <mv^2/2>=mc^2/2.

2. A dice is loaded such that 6 occurs twice as often as 1. Calculate the unbiased probabilities for the 6 faces of the dice.

3. Problem 6.1

4. Problem 6.2

5. Problem 6.6

6. Problem 6.7

7. Problem 6.13