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4

Continuous Random

Variables and

Probability

Distributions

CHAPTER OUTLINE

4-1 CONTINUOUS RANDOM 4-7 NORMAL APPROXIMATION TO
VARIABLES THE BINOMIAL AND POISSON
DISTRIBUTIONS
4-2 PROBABILITY DISTRIBUTIONS
AND PROBABILITY DENSITY 4-8 CONTINUITY CORRECTION TO
FUNCTIONS IMPROVE THE APPROXIMATION
(CD ONLY)
4-3 CUMULATIVE DISTRIBUTION
FUNCTIONS 4-9 EXPONENTIAL DISTRIBUTION
4-4 MEAN AND VARIANCE OF A 4-10 ERLANG AND GAMMA
CONTINUOUS RANDOM DISTRIBUTIONS
VARIABLE
4-10.1 Erlang Distribution
4-5 CONTINUOUS UNIFORM
DISTRIBUTION 4-10.2 Gamma Distribution
4-11 WEIBULL DISTRIBUTION
4-6 NORMAL DISTRIBUTION
4-12 LOGNORMAL DISTRIBUTION

LEARNING OBJECTIVES

After careful study of this chapter you should be able to do the following:
1. Determine probabilities from probability density functions.
2. Determine probabilities from cumulative distribution functions and cumulative distribution func-
tions from probability density functions, and the reverse.
3. Calculate means and variances for continuous random variables.
4. Understand the assumptions for each of the continuous probability distributions presented.
5. Select an appropriate continuous probability distribution to calculate probabilities in specific
applications.
6. Calculate probabilities, determine means and variances for each of the continuous probability
distributions presented.
7. Standardize normal random variables.

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