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Chapter 5: Problem 57

List the five identifying characteristics of the binomial experiment.

Short Answer

Expert verified
Answer: The five identifying characteristics of a binomial experiment are: 1. Fixed number of trials (n) 2. Two mutually exclusive outcomes (success and failure) 3. Constant probabilities (p and q) for each trial 4. Independent trials 5. Random variable denoting the number of successes (X) in the 'n' trials

Step by step solution

01

1. Number of trials

A binomial experiment consists of a fixed number of trials, denoted as 'n'. Each trial is independent of others, and the overall result does not depend on the order of those trials.
02

2. Two possible outcomes

In each trial of a binomial experiment, there can be only two mutually exclusive outcomes: success (usually denoted as 'S') and failure (denoted as 'F'). These two outcomes are complementary.
03

3. Probabilities remain constant

The probability of success (p) and failure (q) remain constant throughout the experiment. The sum of these probabilities is equal to 1, i.e., p + q = 1.
04

4. Independent trials

The trials in a binomial experiment are independent, meaning that the outcome of one trial does not affect the outcomes of other trials. This implies that the probabilities for each trial are not influenced by the outcomes of previous trials.
05

5. Random variable

The random variable associated with a binomial experiment denotes the number of successes in the 'n' trials, denoted as 'X'. The possible values of 'X' range from 0 to n. The binomial probability formula is given by: P(X = k) = C(n, k) * (p^k) * (q^(n-k)), where C(n, k) represents the number of combinations of 'n' items taken 'k' at a time, also represented as n!/(k!*(n-k)!).

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