# 3-1 Discrete Random Variables 3-1 Discrete Random Variables 3-1 Discrete Random Variables 3-1 Discrete Random Variables Example 3-1

3-2 Probability Distributions and Probability Mass Functions

Figure 3-1 Probability distribution for bits in error. 3-2 Probability Distributions and Probability Mass Functions

3-2 Probability Distributions and Probability Mass Functions Definition

Example 3-5 Example 3-5 (continued)

3-3 Cumulative Distribution Functions Definition Example 3-8

Example 3-8 Figure 3-4 Cumulative distribution function for

Example 3-8. 3-4 Mean and Variance of a Discrete Random Variable

Definition 3-4 Mean and Variance of a Discrete Random Variable

Figure 3-5 A probability distribution can be viewed as a loading with the mean equal to the balance point. Parts (a) and (b) illustrate equal means, but Part (a) illustrates a larger variance.

3-4 Mean and Variance of a Discrete Random Variable

Figure 3-6 The probability distribution illustrated in Parts (a) and (b) differ even though they have equal means and equal variances.

Example 3-11 3-4 Mean and Variance of a Discrete Random Variable

Expected Value of a Function of a Discrete Random Variable 3-5 Discrete Uniform Distribution

Definition 3-5 Discrete Uniform Distribution Example 3-13

3-5 Discrete Uniform Distribution Figure 3-7 Probability mass function for a discrete uniform

random variable. 3-5 Discrete Uniform Distribution Mean and Variance

3-6 Binomial Distribution Random experiments and random variables

3-6 Binomial Distribution Random experiments and random variables 3-6 Binomial Distribution

Definition 3-6 Binomial Distribution

Figure 3-8 Binomial distributions for selected values of n and p. 3-6 Binomial Distribution

Example 3-18 3-6 Binomial Distribution Example 3-18

3-6 Binomial Distribution Mean and Variance

3-6 Binomial Distribution Example 3-19 3-7 Geometric and Negative Binomial

Distributions Example 3-20 3-7 Geometric and Negative Binomial

Distributions Definition 3-7 Geometric and Negative Binomial

Distributions Figure 3-9. Geometric distributions for selected values of the parameter p.

3-7 Geometric and Negative Binomial Distributions 3-7.1 Geometric Distribution

Example 3-21 3-7 Geometric and Negative Binomial Distributions

Definition 3-7 Geometric and Negative Binomial Distributions

Lack of Memory Property 3-7 Geometric and Negative Binomial Distributions

3-7.2 Negative Binomial Distribution 3-7 Geometric and Negative Binomial Distributions

Figure 3-10. Negative binomial distributions for selected values of

the parameters r and p. 3-7 Geometric and Negative Binomial

Distributions Figure 3-11. Negative binomial random variable represented as a sum of geometric random variables.

3-7 Geometric and Negative Binomial Distributions 3-7.2 Negative Binomial Distribution

3-7 Geometric and Negative Binomial Distributions Example 3-25

3-7 Geometric and Negative Binomial Distributions Example 3-25

3-8 Hypergeometric Distribution Definition

3-8 Hypergeometric Distribution Figure 3-12. Hypergeometric distributions for

selected values of parameters N, K, and n. 3-8 Hypergeometric Distribution

Example 3-27 3-8 Hypergeometric Distribution Example 3-27

3-8 Hypergeometric Distribution Mean and Variance

3-8 Hypergeometric Distribution Finite Population Correction Factor 3-8 Hypergeometric Distribution

Figure 3-13. Comparison of hypergeometric and binomial distributions.

3-9 Poisson Distribution Example 3-30 3-9 Poisson Distribution

Definition 3-9 Poisson Distribution Consistent Units

3-9 Poisson Distribution Example 3-33

3-9 Poisson Distribution Example 3-33 3-9 Poisson Distribution

Mean and Variance