251hwkpatch2 3/11/03
J. Random Variables.
1. Definitions.
2. Probability Distribution of a Discrete Random Variable.
3. Expected Value (Expectation) of a Discrete Random Variable.
D&C pg. 130 means for 1 - 4. J0A, J1.
4. Variance of a Discrete Random Variable.
D&C pg. 130 standard deviations for 1 - 4. J0B, Text 5.3, 5.4, 5.8. J2-J4.
5. Summary
J6, J7
6. Continuous Random Variables.
a. Normal Distribution (Overview).
b. The Continuous Uniform Distribution.
J8. J10(New problem.)
c. Cumulative Distributions, Means and Variances for Continuous Distributions.
d. Chebyschev's Inequality Again.
J9.
7. Skewness and Kurtosis (Short Summary).
L. Discrete Distributions.
1. Binomial Distribution.
L1. Text 5.15, 5.18, 5.19.
2. Geometric Distribution.
L2-L5.
3. Poisson Distribution.
L6-L8. Text 5.22 - 5.25.
4. Hypergeometric Distribution.
Text 5.30, 5.31, 5.35, 5.36. L9, L10. Graded Assignment 3.
distribution.
Note that problem L11 is a review of the continuous uniform
PROBLEM J0A. Flip a coin 4 times. Let x be the number of heads. Find the following:
a. The distribution of x .
b. Find the probability of (i) at least one head, (ii) An even number of heads, (iii) at least 2 heads.
c. Find E x 
PROBLEM J0B.
In problem J0A find the standard deviation of the number of heads
PROBLEM J10. Find P8  x  12  for the following distributions
a. Continuous Uniform with c  3, d  27 (Make a diagram!).
b. Continuous Uniform with c  3, d  10 (Make a diagram!).
Find these areas in two ways. First, make an appropriate diagram and find the area of the box. Second, use
the cumulative distribution to find P8  x  12   F 12   F 8 .
PROBLEM L11. Find the probability P5  x  13 for
a) A continuous uniform distribution with c  1, d  21
b) A continuous uniform distribution with c  1, d  11
c) A continuous uniform distribution with c  11, d  21