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In uniform distribution random variable xiims only the value eight nine 11 15 18 20 then p of x is equal to 9 each?
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In uniform distribution random variable xiims only the value eight nin...
Understanding Uniform Distribution
Uniform distribution is a type of probability distribution where every outcome has an equal chance of occurring. When we have a discrete set of values, such as 8, 9, 11, 15, 18, and 20, we can analyze the probability of each value.
Given Values
- The random variable \( X \) can take the values:
- 8
- 9
- 11
- 15
- 18
- 20
Total Outcomes
- There are **6 distinct outcomes** in this case.
Calculating Probability
- In a uniform distribution, the probability of each outcome is calculated as:
\[
P(X = x_i) = \frac{1}{n}
\]
- Here, \( n \) is the total number of outcomes. Thus:
\[
P(X = 8) = P(X = 9) = P(X = 11) = P(X = 15) = P(X = 18) = P(X = 20) = \frac{1}{6}
\]
Conclusion
- Hence, the probability of each value, including \( P(X = 9) \), is **1/6** or approximately **0.1667**.
- This means that each value from the set has an equal likelihood of occurring, confirming the principle of uniform distribution.
Key Takeaway
- All values in this uniform distribution, including 9, indeed share the same probability, which is **1/6**.
Uniform distribution is a type of probability distribution where every outcome has an equal chance of occurring. When we have a discrete set of values, such as 8, 9, 11, 15, 18, and 20, we can analyze the probability of each value.
Given Values
- The random variable \( X \) can take the values:
- 8
- 9
- 11
- 15
- 18
- 20
Total Outcomes
- There are **6 distinct outcomes** in this case.
Calculating Probability
- In a uniform distribution, the probability of each outcome is calculated as:
\[
P(X = x_i) = \frac{1}{n}
\]
- Here, \( n \) is the total number of outcomes. Thus:
\[
P(X = 8) = P(X = 9) = P(X = 11) = P(X = 15) = P(X = 18) = P(X = 20) = \frac{1}{6}
\]
Conclusion
- Hence, the probability of each value, including \( P(X = 9) \), is **1/6** or approximately **0.1667**.
- This means that each value from the set has an equal likelihood of occurring, confirming the principle of uniform distribution.
Key Takeaway
- All values in this uniform distribution, including 9, indeed share the same probability, which is **1/6**.
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In uniform distribution random variable xiims only the value eight nine 11 15 18 20 then p of x is equal to 9 each?
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In uniform distribution random variable xiims only the value eight nine 11 15 18 20 then p of x is equal to 9 each? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In uniform distribution random variable xiims only the value eight nine 11 15 18 20 then p of x is equal to 9 each? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In uniform distribution random variable xiims only the value eight nine 11 15 18 20 then p of x is equal to 9 each?.
In uniform distribution random variable xiims only the value eight nine 11 15 18 20 then p of x is equal to 9 each? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In uniform distribution random variable xiims only the value eight nine 11 15 18 20 then p of x is equal to 9 each? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In uniform distribution random variable xiims only the value eight nine 11 15 18 20 then p of x is equal to 9 each?.
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