Answer:
Let's analyze the two random variables:
1. Drawing 5 cards from a deck, and x is the random variable counting the number of Aces drawn:
- Random Variable: x (Number of Aces drawn)
- Realizations: x can take values from 0 (no Aces) to 5 (all Aces) because there are only 4 Aces in a standard deck of 52 cards, and you are drawing 5 cards.
- Type: This is a discrete random variable because the possible values are distinct integers (0, 1, 2, 3, 4, 5), and you cannot draw a fractional or continuous number of Aces.
2. Taking a 60-minute test, and x is the random variable observing the time it takes to finish the test:
- Random Variable: x (Time taken to finish the test)
- Realizations: x can take any real number between 0 and 60, as time can vary continuously within this range. For example, it can be 25.5 minutes, 42.75 minutes, etc.
- Type: This is a continuous random variable because it can take on an infinite number of values within the specified range (0 to 60 minutes), and you can have fractional values indicating the exact time it takes to finish the test.
Explanation: