2.1.2 Examples of Random Variables¶
Example 1: Sales Calls¶
- Situation: Making sales calls to five customers, where each outcome (placing an order) is random.
- Random Variable: Number of orders received from five calls.
- Values: Can be 0, 1, 2, 3, 4, or 5.
- Type: Discrete Random Variable.
Example 2: Defective Radios¶
- Situation: Receiving a shipment of 50 radios from a supplier, some of which may be defective.
- Random Variable: Number of defective radios in the shipment.
- Values: Ranges from 0 to 50.
- Type: Discrete Random Variable.
Example 3: Restaurant Customers¶
- Situation: Counting the number of customers coming to a restaurant on any given day.
- Random Variable: Number of customers per day.
- Values: Can technically range up to infinity.
- Type: Discrete Random Variable.
Example 4: Time Between Bank Customers¶
- Situation: Observing the time between arrivals of consecutive customers at a bank.
- Random Variable: Time between arrivals.
- Values: Any positive number (time in minutes or seconds).
- Type: Continuous Random Variable.
Example 5: Soft Drink Can Volume¶
- Situation: A soft drink can is marked to contain 12 ounces of fluid.
- Random Variable: Actual amount of fluid in the can.
- Values: Could vary between 11.5 to 12.5 fluid ounces.
- Type: Continuous Random Variable.
Example 6: Chemical Reaction Temperature¶
- Situation: A chemical process where a reaction is desired at a certain temperature.
- Random Variable: Temperature at which the reaction takes place.
- Values: Between 100 degrees centigrade and 150 degrees centigrade.
- Type: Continuous Random Variable.
Key Concepts¶
- Probability Mass Function (PMF): For discrete random variables, denotes the probability of taking a specific value.
- Examples in Plots:
- For a fair die, PMF is uniform (1/6 for each side).
- For a biased die, PMF varies by the probability of each side.
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