CA Foundation Exam > CA Foundation Questions > For a Poisson variate X, P(X = 1) = P (X = 2)...
Start Learning for Free
For a Poisson variate X, P(X = 1) = P (X = 2). What is the mean of X?
- a)1.00
- b)1.50
- c)2.00
- d)2.50
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
For a Poisson variate X, P(X = 1) = P (X = 2). What is the mean of X?a...
Explanation:
To find the mean of a Poisson distribution, we need to use the formula:
Mean (μ) = λ
Where λ is the rate parameter of the Poisson distribution.
In this question, we are given that P(X = 1) = P(X = 2), which means that the probability of observing one event is the same as the probability of observing two events. Let's denote this probability as p:
P(X = 1) = p
P(X = 2) = p
We know that the sum of probabilities for all possible values of X in a Poisson distribution is equal to 1. Therefore, we can write the equation:
P(X = 0) + P(X = 1) + P(X = 2) + ...
Since P(X = 1) = P(X = 2), we can rewrite the equation as:
P(X = 0) + P(X = 1) + P(X = 1) + ...
Simplifying further:
P(X = 0) + 2P(X = 1) + ...
We can see that the sum of probabilities for all possible values of X will be greater than 1, which is not possible. Hence, the only way for this equation to hold true is if P(X = 0) = 0.
Now, we can use the formula for the mean of a Poisson distribution:
Mean (μ) = λ
Since P(X = 0) = 0, it means that the rate parameter λ is not equal to zero. Therefore, the mean of X is equal to λ, which is the rate parameter.
Hence, the correct answer is option 'C' (2.00).
To find the mean of a Poisson distribution, we need to use the formula:
Mean (μ) = λ
Where λ is the rate parameter of the Poisson distribution.
In this question, we are given that P(X = 1) = P(X = 2), which means that the probability of observing one event is the same as the probability of observing two events. Let's denote this probability as p:
P(X = 1) = p
P(X = 2) = p
We know that the sum of probabilities for all possible values of X in a Poisson distribution is equal to 1. Therefore, we can write the equation:
P(X = 0) + P(X = 1) + P(X = 2) + ...
Since P(X = 1) = P(X = 2), we can rewrite the equation as:
P(X = 0) + P(X = 1) + P(X = 1) + ...
Simplifying further:
P(X = 0) + 2P(X = 1) + ...
We can see that the sum of probabilities for all possible values of X will be greater than 1, which is not possible. Hence, the only way for this equation to hold true is if P(X = 0) = 0.
Now, we can use the formula for the mean of a Poisson distribution:
Mean (μ) = λ
Since P(X = 0) = 0, it means that the rate parameter λ is not equal to zero. Therefore, the mean of X is equal to λ, which is the rate parameter.
Hence, the correct answer is option 'C' (2.00).
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
For a Poisson variate X, P(X = 1) = P (X = 2). What is the mean of X?a)1.00b)1.50c)2.00d)2.50Correct answer is option 'C'. Can you explain this answer?
Question Description
For a Poisson variate X, P(X = 1) = P (X = 2). What is the mean of X?a)1.00b)1.50c)2.00d)2.50Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about For a Poisson variate X, P(X = 1) = P (X = 2). What is the mean of X?a)1.00b)1.50c)2.00d)2.50Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a Poisson variate X, P(X = 1) = P (X = 2). What is the mean of X?a)1.00b)1.50c)2.00d)2.50Correct answer is option 'C'. Can you explain this answer?.
For a Poisson variate X, P(X = 1) = P (X = 2). What is the mean of X?a)1.00b)1.50c)2.00d)2.50Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about For a Poisson variate X, P(X = 1) = P (X = 2). What is the mean of X?a)1.00b)1.50c)2.00d)2.50Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a Poisson variate X, P(X = 1) = P (X = 2). What is the mean of X?a)1.00b)1.50c)2.00d)2.50Correct answer is option 'C'. Can you explain this answer?.
Solutions for For a Poisson variate X, P(X = 1) = P (X = 2). What is the mean of X?a)1.00b)1.50c)2.00d)2.50Correct 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 For a Poisson variate X, P(X = 1) = P (X = 2). What is the mean of X?a)1.00b)1.50c)2.00d)2.50Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
For a Poisson variate X, P(X = 1) = P (X = 2). What is the mean of X?a)1.00b)1.50c)2.00d)2.50Correct answer is option 'C'. Can you explain this answer?, a detailed solution for For a Poisson variate X, P(X = 1) = P (X = 2). What is the mean of X?a)1.00b)1.50c)2.00d)2.50Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of For a Poisson variate X, P(X = 1) = P (X = 2). What is the mean of X?a)1.00b)1.50c)2.00d)2.50Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice For a Poisson variate X, P(X = 1) = P (X = 2). What is the mean of X?a)1.00b)1.50c)2.00d)2.50Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup