Help Understanding Probability: Random Variables & Coin Flips

In summary, the sample space can be represented by assigning different values to each event, as shown in the example with flipping coins. The number 17 is arbitrary and can be replaced with any other number.
  • #1
vincentvance
9
0
I'm going through examples in my textbook in probability and found one that I just can't follow, so I'm wondering if someone might be able to help me.

Ex:
If the sample space corresponds to flipping three different coins, then we could let X be the total number of heads showing, let Y be the total number of tails showing, let Z = 0 if there is exactly one head, and otherwise Z = 17, etc.

I don't get where the 17 came from. Why is Z = 17 when there isn't exactly one head and what are they referring to when they say "etc"? Does anyone know?
 
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  • #2
The 17 is arbitrary and can be replaced with any number. What the exercise is suggesting is that you assign different values to each event in the sample space (in this case, the different outcomes of flipping three coins). So, in this example, X would be the number of heads showing, Y would be the number of tails showing, and Z would be 0 if there is exactly one head, and 17 if there isn't. The "etc" implies that you can assign any value to each event.
 

Related to Help Understanding Probability: Random Variables & Coin Flips

1. What is probability and how is it related to random variables?

Probability is a measure of the likelihood of a certain event occurring. It is related to random variables because random variables are used to represent uncertain outcomes in a probability distribution.

2. How do you calculate the probability of getting a specific outcome from a coin flip?

The probability of getting a specific outcome from a coin flip is calculated by dividing the number of desired outcomes by the total number of possible outcomes. For example, the probability of getting heads on a coin flip is 1/2 or 50% because there is only one desired outcome (heads) out of two possible outcomes (heads or tails).

3. What is the difference between a discrete and a continuous random variable?

A discrete random variable can only take on a finite or countably infinite number of values, while a continuous random variable can take on any value within a certain range. For example, the number of heads obtained in 5 coin flips is a discrete random variable, while the height of a randomly selected person is a continuous random variable.

4. How do you use a probability distribution to understand the likelihood of different outcomes in a coin flip experiment?

A probability distribution is a function that assigns probabilities to each possible outcome in a random variable. In a coin flip experiment, the probability distribution would show the likelihood of obtaining each outcome (heads or tails) and can be used to predict the frequency of each outcome in a large number of trials.

5. How can understanding probability and random variables be useful in real life situations?

Understanding probability and random variables can be useful in real life situations in many ways. For example, it can help in making informed decisions based on the likelihood of certain outcomes, such as in gambling or investing. It can also be used in predicting and managing risk, such as in insurance and finance. Additionally, probability and random variables are essential in many scientific fields, such as physics, biology, and psychology, where they are used to model and analyze complex systems and phenomena.

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