Multiple Choice
Given the following table showing the possible values of a random variable and their probabilities: Value of : 0, 1, 2; Probability: 0.2, 0.5, 0.3. Is the random variable discrete or continuous? Explain your answer.
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5. Binomial Distribution & Discrete Random Variables
Discrete Random Variables
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Which of the following is a criterion for a binomial probability experiment?
A
Each trial results in exactly possible outcomes, commonly labeled as success and failure.
B
Each trial must have a different probability of success.
C
The number of trials can be .
D
The probability of success must increase with each trial.
Verified step by step guidance1
Understand that a binomial probability experiment is a specific type of probability experiment characterized by certain criteria.
Recall the key criteria for a binomial experiment: (1) The experiment consists of a fixed number of trials, (2) Each trial is independent, (3) Each trial results in exactly two possible outcomes (success or failure), and (4) The probability of success remains constant for each trial.
Evaluate each option against these criteria: The correct criterion must state that each trial results in exactly two possible outcomes, commonly labeled as success and failure.
Recognize that options stating the probability changes or the number of trials is infinite do not meet the binomial experiment requirements, as the probability must be constant and the number of trials fixed.
Conclude that the correct criterion is the one stating that each trial results in exactly two possible outcomes, success and failure.
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