Podcast
Questions and Answers
What is the probability that exactly one man will live through the next year?
What is the probability that exactly one man will live through the next year?
0.0001
What is the probability that at least one man will live through the next year?
What is the probability that at least one man will live through the next year?
0.9999
What is the probability that fewer than two men will live through the next year?
What is the probability that fewer than two men will live through the next year?
0.0007
What is the first step in calculating the mean of the given probability distribution?
What is the first step in calculating the mean of the given probability distribution?
Which formula is used to calculate the variance from the probability distribution?
Which formula is used to calculate the variance from the probability distribution?
What aspect of the probability distribution does the standard deviation measure?
What aspect of the probability distribution does the standard deviation measure?
If the mean of the probability distribution is found to be 3.923, what will be the result when calculating the variance using the mean?
If the mean of the probability distribution is found to be 3.923, what will be the result when calculating the variance using the mean?
What is the relationship between the expected value and the mean in this probability distribution?
What is the relationship between the expected value and the mean in this probability distribution?
Flashcards
Probability Distribution
Probability Distribution
A table or function that shows the probability of each possible outcome for a variable.
Mean (Expected Value)
Mean (Expected Value)
The average value of a random variable, calculated by summing each outcome multiplied by its probability.
Standard Deviation
Standard Deviation
A measure of the spread or dispersion of a probability distribution.
Variance
Variance
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Probability
Probability
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Outcome
Outcome
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x
x
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P(x)
P(x)
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Expected Value formula
Expected Value formula
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Variance formula
Variance formula
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Standard Deviation calculation
Standard Deviation calculation
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Spreadsheet Software
Spreadsheet Software
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Calculator
Calculator
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∑
∑
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Random Variable
Random Variable
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Probability data
Probability data
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Numerical outcome
Numerical outcome
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Random Phenomenon
Random Phenomenon
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Probability Distribution Table
Probability Distribution Table
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Calculating mean from a probability table
Calculating mean from a probability table
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Calculating standard deviation from a probability table
Calculating standard deviation from a probability table
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Calculate Expected Value
Calculate Expected Value
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Spread out data?
Spread out data?
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Study Notes
Probability of Exactly One Man Living Through the Year
- This probability requires calculating the chances of one man living and the other dying, while also accounting for which man survives
- There are two possible scenarios:
- Man 1 lives, Man 2 dies
- Man 1 dies, Man 2 lives
- Each scenario needs to be calculated individually and then added together
Probability of At Least One Man Living Through the Year
- This probability covers all scenarios where at least one man survives
- It can be calculated directly by finding the probability of the opposite scenario happening (both men dying) and subtracting it from 1 (certainty)
Probability of Fewer Than Two Men Living Through the Year
- This probability covers scenarios where zero or one man survives
- This can be calculated by:
- Finding the probability of both men dying
- Adding it to the probability of exactly one man living (calculated previously)
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