CA Foundation Exam > CA Foundation Questions > In a discrete random variable x follows unifo...
Start Learning for Free
In a discrete random variable x follows uniform distribution and assumes only the values 8, 9, 11, 15, 18, 20. Then P(|x – 14| < 5) is
- a)1/3
- b)2/3
- c)1/2
- d)1
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
In a discrete random variable x follows uniform distribution and assum...
Uniform Distribution
- In a uniform distribution, all outcomes have an equal probability of occurring.
- In this case, the random variable x follows a uniform distribution and assumes the values 8, 9, 11, 15, 18, and 20.
Calculating the Probability
- We need to find the probability that the absolute difference between x and 14 is greater than 5.
- So we need to find P(|x - 14| > 5).
Calculating P(x < 9="" or="" x="" /> 19)
- To calculate this probability, we need to find the probability of x being less than 9 or greater than 19.
- Since the distribution is uniform, the probability of each outcome is 1/6.
Calculating P(x < />
- There are two outcomes (8 and 9) that are less than 9, so the probability of x being less than 9 is 2/6.
Calculating P(x > 19)
- There are two outcomes (18 and 20) that are greater than 19, so the probability of x being greater than 19 is also 2/6.
Calculating P(|x - 14| > 5)
- We can find this probability by subtracting the probability of x being between 9 and 19 from 1.
- The probability of x being between 9 and 19 is the complement of the probability of x being less than 9 or greater than 19.
- P(x between 9 and 19) = 1 - P(x < 9)="" -="" p(x="" /> 19)
- P(x between 9 and 19) = 1 - 2/6 - 2/6
- P(x between 9 and 19) = 1 - 4/6
- P(x between 9 and 19) = 2/6
Calculating P(|x - 14| > 5)
- P(|x - 14| > 5) = 1 - P(x between 9 and 19)
- P(|x - 14| > 5) = 1 - 2/6
- P(|x - 14| > 5) = 4/6
- P(|x - 14| > 5) = 2/3
Conclusion
- Therefore, the probability P(|x - 14| > 5) is 2/3, which is option B.
- In a uniform distribution, all outcomes have an equal probability of occurring.
- In this case, the random variable x follows a uniform distribution and assumes the values 8, 9, 11, 15, 18, and 20.
Calculating the Probability
- We need to find the probability that the absolute difference between x and 14 is greater than 5.
- So we need to find P(|x - 14| > 5).
Calculating P(x < 9="" or="" x="" /> 19)
- To calculate this probability, we need to find the probability of x being less than 9 or greater than 19.
- Since the distribution is uniform, the probability of each outcome is 1/6.
Calculating P(x < />
- There are two outcomes (8 and 9) that are less than 9, so the probability of x being less than 9 is 2/6.
Calculating P(x > 19)
- There are two outcomes (18 and 20) that are greater than 19, so the probability of x being greater than 19 is also 2/6.
Calculating P(|x - 14| > 5)
- We can find this probability by subtracting the probability of x being between 9 and 19 from 1.
- The probability of x being between 9 and 19 is the complement of the probability of x being less than 9 or greater than 19.
- P(x between 9 and 19) = 1 - P(x < 9)="" -="" p(x="" /> 19)
- P(x between 9 and 19) = 1 - 2/6 - 2/6
- P(x between 9 and 19) = 1 - 4/6
- P(x between 9 and 19) = 2/6
Calculating P(|x - 14| > 5)
- P(|x - 14| > 5) = 1 - P(x between 9 and 19)
- P(|x - 14| > 5) = 1 - 2/6
- P(|x - 14| > 5) = 4/6
- P(|x - 14| > 5) = 2/3
Conclusion
- Therefore, the probability P(|x - 14| > 5) is 2/3, which is option B.
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
In a discrete random variable x follows uniform distribution and assumes only the values 8, 9, 11, 15, 18, 20. Then P(|x – 14| < 5) isa)1/3b)2/3c)1/2d)1Correct answer is option 'C'. Can you explain this answer?
Question Description
In a discrete random variable x follows uniform distribution and assumes only the values 8, 9, 11, 15, 18, 20. Then P(|x – 14| < 5) isa)1/3b)2/3c)1/2d)1Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about In a discrete random variable x follows uniform distribution and assumes only the values 8, 9, 11, 15, 18, 20. Then P(|x – 14| < 5) isa)1/3b)2/3c)1/2d)1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a discrete random variable x follows uniform distribution and assumes only the values 8, 9, 11, 15, 18, 20. Then P(|x – 14| < 5) isa)1/3b)2/3c)1/2d)1Correct answer is option 'C'. Can you explain this answer?.
In a discrete random variable x follows uniform distribution and assumes only the values 8, 9, 11, 15, 18, 20. Then P(|x – 14| < 5) isa)1/3b)2/3c)1/2d)1Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about In a discrete random variable x follows uniform distribution and assumes only the values 8, 9, 11, 15, 18, 20. Then P(|x – 14| < 5) isa)1/3b)2/3c)1/2d)1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a discrete random variable x follows uniform distribution and assumes only the values 8, 9, 11, 15, 18, 20. Then P(|x – 14| < 5) isa)1/3b)2/3c)1/2d)1Correct answer is option 'C'. Can you explain this answer?.
Solutions for In a discrete random variable x follows uniform distribution and assumes only the values 8, 9, 11, 15, 18, 20. Then P(|x – 14| < 5) isa)1/3b)2/3c)1/2d)1Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of In a discrete random variable x follows uniform distribution and assumes only the values 8, 9, 11, 15, 18, 20. Then P(|x – 14| < 5) isa)1/3b)2/3c)1/2d)1Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In a discrete random variable x follows uniform distribution and assumes only the values 8, 9, 11, 15, 18, 20. Then P(|x – 14| < 5) isa)1/3b)2/3c)1/2d)1Correct answer is option 'C'. Can you explain this answer?, a detailed solution for In a discrete random variable x follows uniform distribution and assumes only the values 8, 9, 11, 15, 18, 20. Then P(|x – 14| < 5) isa)1/3b)2/3c)1/2d)1Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of In a discrete random variable x follows uniform distribution and assumes only the values 8, 9, 11, 15, 18, 20. Then P(|x – 14| < 5) isa)1/3b)2/3c)1/2d)1Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In a discrete random variable x follows uniform distribution and assumes only the values 8, 9, 11, 15, 18, 20. Then P(|x – 14| < 5) isa)1/3b)2/3c)1/2d)1Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup