I need some help with some probability

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In summary, for general expected value, you multiply the probability of X to the value of X and add them up. For density function, such as f(x) = 2x 0<x<1 and 0 otherwise, you take the integral. For a continuous random variable, like f(x) = (x - 8) 8 < x < 9; (10 -x ) 9 < x < 10; 0 otherwise, we can define f(9)=1 and the expected value is the sum of the areas under the curve. The expected value for this question is 1, proving that f is a probability function.
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hellosonic
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So for general expected value, I know how to do it. Multiply probablity of X to the value of X and add them up. For density function such as

f(x) = 2x 0<x<1 and 0 otherwise. I take find the integral. I'm just confused when it comes to something like

f(x) = (x - 8) 8 < x < 9; (10 -x ) 9 < x < 10; 0 otherwise. I hope someone can help me clear this up lolz. Thanks veryyyyyy much
 
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Here since this is continuous random variable, we can define f(9)=1. Then looking at the graph of x-f(x), we see that the expected value is the sum of the areas under the curve. Hence, for this question the expected value is ((10-8)*1)/2=1, which proves that f is a probability function.
 

1. What is probability and how is it calculated?

Probability is a measure of the likelihood of an event occurring. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

2. How is probability used in scientific research?

Probability is used in scientific research to determine the likelihood of certain outcomes, to make predictions, and to analyze data. It is also used to test hypotheses and draw conclusions about the relationship between variables.

3. What is the difference between theoretical and experimental probability?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Experimental probability is based on actual data collected through experiments or observations, which may not always result in equal likelihood of outcomes.

4. Can probability be greater than 1 or less than 0?

No, probability cannot be greater than 1 or less than 0. A probability of 1 means that the event is certain to occur, while a probability of 0 means that the event is impossible. All probabilities must fall between 0 and 1.

5. How can probability be applied in everyday life?

Probability can be applied in everyday life in various ways, such as making decisions based on likelihood, understanding risk and uncertainty, and interpreting statistics and data. It can also be used in fields like finance, sports, and gambling.

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