Algebra: Show that v, ø(v), ø(v)^2 are independent

In summary, showing that v, ø(v), and ø(v)^2 are independent in algebra means that they are not related or dependent on each other. It is important to demonstrate this independence in order to better understand relationships between variables and avoid making incorrect assumptions. To prove this independence, one can use the definition or algebraic manipulation. Some common examples of independent variables in algebra include distance and time, height and weight, and temperature and pressure. However, there can be exceptions to this rule, so it is important to carefully analyze data and consider all possible factors.
  • #1
victoranderson
34
0
Please see attached question.
I can finish part (a)

For part b, how can I find ø(v) ?
Although I can find ø(v1) and ø(v2) but I think it is unrelated to ø(v)...
 
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  • #2
I am sorry for creating two posts accidentally, I am just a newbie...
 

FAQ: Algebra: Show that v, ø(v), ø(v)^2 are independent

1. What does it mean to show that v, ø(v), and ø(v)^2 are independent in algebra?

Showing that v, ø(v), and ø(v)^2 are independent in algebra means that they are not related or dependent on each other in any way. This means that the values of one variable cannot be predicted or determined by the values of the other variables.

2. Why is it important to demonstrate that v, ø(v), and ø(v)^2 are independent in algebra?

Demonstrating that v, ø(v), and ø(v)^2 are independent is important because it allows us to better understand the relationships between variables and make accurate predictions or calculations. It also helps to avoid making incorrect assumptions or conclusions based on the values of one variable.

3. How can I prove that v, ø(v), and ø(v)^2 are independent in algebra?

To prove that v, ø(v), and ø(v)^2 are independent in algebra, you can use the definition of independence which states that if the joint probability of two variables is equal to the product of their individual probabilities, then the variables are independent. You can also use algebraic manipulation and substitution to show that the values of one variable are not dependent on the values of the other variables.

4. What are some examples of variables that are commonly shown to be independent in algebra?

Some common examples of variables that are shown to be independent in algebra include distance and time, height and weight, and temperature and pressure. These variables have no direct effect on each other and can be manipulated independently.

5. Are there any exceptions to the rule that v, ø(v), and ø(v)^2 are independent in algebra?

Yes, there can be exceptions to the rule that v, ø(v), and ø(v)^2 are independent in algebra. In some cases, there may be hidden variables or factors that affect the relationships between these variables. It is important to carefully analyze the data and consider all possible factors before concluding that variables are truly independent.

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