CA Foundation Exam > CA Foundation Questions > X is a binomial variable such that 2 P(X = 2)...
Start Learning for Free
X is a binomial variable such that 2 P(X = 2) = P( x = 2) and mean of X is known to be 10/3. What would be the probability that X assumes at most the value 2?
- a)16/81
- b)17/81
- c)47/243
- d)46/243
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
X is a binomial variable such that 2 P(X = 2) = P( x = 2) and mean of ...
Given:
- 2 P(X = 2) = P( x = 2)
- Mean of X = 10/3
- To find: P(X ≤ 2)
Solution:
Let n be the number of trials and p be the probability of success in each trial. Then, from the given information, we have:
- E(X) = np = 10/3
- 2P(X = 2) = P(X = 2)
Using the formula for the mean of a binomial distribution, we get:
np = E(X) = (2P(X = 2) + 2P(X > 2))n
Simplifying this equation using the given information, we get:
(4/3) = (2P(X > 2))n
Also, we know that the probability of X assuming at most the value 2 is:
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
Using the formula for the binomial distribution, we get:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
Substituting the given information, we get:
P(X ≤ 2) = (n choose 0) * p^0 * (1-p)^n + (n choose 1) * p^1 * (1-p)^(n-1) + (n choose 2) * p^2 * (1-p)^(n-2)
= (1-p)^n + np(1-p)^(n-1) + (n(n-1)/2)p^2 (1-p)^(n-2)
Substituting the value of (4/3) for np in the above equation, we get:
P(X ≤ 2) = (1-p)^n + 4/3(1-p)^(n-1) + (n(n-1)/2)(4/9)p^2 (1-p)^(n-2)
We need to solve for p and n in terms of the given information. One way to do this is to use the fact that 2P(X = 2) = P(X = 2), which implies:
2(n choose 2) * p^2 * (1-p)^(n-2) = (n choose 2) * p^2 * (1-p)^(n-2)
Simplifying this equation, we get:
2(n-1)(n-2)p^2 = (n-2)(n-1)p^2
Dividing both sides by (n-1)(n-2)p^2, we get:
2 = 1/(n-2)
Solving for n, we get n = 3. Substituting this value into the equation (4/3) = (2P(X > 2))n, we get:
P(X > 2) = 1/3
Substituting the values of p and n into the expression for P(X ≤ 2), we get:
P(X ≤ 2) = (1-p)^n + np(1-p)^(n-1) + (n(n-1)/2)p^2 (1-p)^(n-2)
= (1-1
- 2 P(X = 2) = P( x = 2)
- Mean of X = 10/3
- To find: P(X ≤ 2)
Solution:
Let n be the number of trials and p be the probability of success in each trial. Then, from the given information, we have:
- E(X) = np = 10/3
- 2P(X = 2) = P(X = 2)
Using the formula for the mean of a binomial distribution, we get:
np = E(X) = (2P(X = 2) + 2P(X > 2))n
Simplifying this equation using the given information, we get:
(4/3) = (2P(X > 2))n
Also, we know that the probability of X assuming at most the value 2 is:
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
Using the formula for the binomial distribution, we get:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
Substituting the given information, we get:
P(X ≤ 2) = (n choose 0) * p^0 * (1-p)^n + (n choose 1) * p^1 * (1-p)^(n-1) + (n choose 2) * p^2 * (1-p)^(n-2)
= (1-p)^n + np(1-p)^(n-1) + (n(n-1)/2)p^2 (1-p)^(n-2)
Substituting the value of (4/3) for np in the above equation, we get:
P(X ≤ 2) = (1-p)^n + 4/3(1-p)^(n-1) + (n(n-1)/2)(4/9)p^2 (1-p)^(n-2)
We need to solve for p and n in terms of the given information. One way to do this is to use the fact that 2P(X = 2) = P(X = 2), which implies:
2(n choose 2) * p^2 * (1-p)^(n-2) = (n choose 2) * p^2 * (1-p)^(n-2)
Simplifying this equation, we get:
2(n-1)(n-2)p^2 = (n-2)(n-1)p^2
Dividing both sides by (n-1)(n-2)p^2, we get:
2 = 1/(n-2)
Solving for n, we get n = 3. Substituting this value into the equation (4/3) = (2P(X > 2))n, we get:
P(X > 2) = 1/3
Substituting the values of p and n into the expression for P(X ≤ 2), we get:
P(X ≤ 2) = (1-p)^n + np(1-p)^(n-1) + (n(n-1)/2)p^2 (1-p)^(n-2)
= (1-1
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
X is a binomial variable such that 2 P(X = 2) = P( x = 2) and mean of X is known to be 10/3. What would be the probability that X assumes at most the value 2?a)16/81b)17/81c)47/243d)46/243Correct answer is option 'B'. Can you explain this answer?
Question Description
X is a binomial variable such that 2 P(X = 2) = P( x = 2) and mean of X is known to be 10/3. What would be the probability that X assumes at most the value 2?a)16/81b)17/81c)47/243d)46/243Correct answer is option 'B'. 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 X is a binomial variable such that 2 P(X = 2) = P( x = 2) and mean of X is known to be 10/3. What would be the probability that X assumes at most the value 2?a)16/81b)17/81c)47/243d)46/243Correct answer is option 'B'. 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 X is a binomial variable such that 2 P(X = 2) = P( x = 2) and mean of X is known to be 10/3. What would be the probability that X assumes at most the value 2?a)16/81b)17/81c)47/243d)46/243Correct answer is option 'B'. Can you explain this answer?.
X is a binomial variable such that 2 P(X = 2) = P( x = 2) and mean of X is known to be 10/3. What would be the probability that X assumes at most the value 2?a)16/81b)17/81c)47/243d)46/243Correct answer is option 'B'. 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 X is a binomial variable such that 2 P(X = 2) = P( x = 2) and mean of X is known to be 10/3. What would be the probability that X assumes at most the value 2?a)16/81b)17/81c)47/243d)46/243Correct answer is option 'B'. 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 X is a binomial variable such that 2 P(X = 2) = P( x = 2) and mean of X is known to be 10/3. What would be the probability that X assumes at most the value 2?a)16/81b)17/81c)47/243d)46/243Correct answer is option 'B'. Can you explain this answer?.
Solutions for X is a binomial variable such that 2 P(X = 2) = P( x = 2) and mean of X is known to be 10/3. What would be the probability that X assumes at most the value 2?a)16/81b)17/81c)47/243d)46/243Correct answer is option 'B'. 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 X is a binomial variable such that 2 P(X = 2) = P( x = 2) and mean of X is known to be 10/3. What would be the probability that X assumes at most the value 2?a)16/81b)17/81c)47/243d)46/243Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
X is a binomial variable such that 2 P(X = 2) = P( x = 2) and mean of X is known to be 10/3. What would be the probability that X assumes at most the value 2?a)16/81b)17/81c)47/243d)46/243Correct answer is option 'B'. Can you explain this answer?, a detailed solution for X is a binomial variable such that 2 P(X = 2) = P( x = 2) and mean of X is known to be 10/3. What would be the probability that X assumes at most the value 2?a)16/81b)17/81c)47/243d)46/243Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of X is a binomial variable such that 2 P(X = 2) = P( x = 2) and mean of X is known to be 10/3. What would be the probability that X assumes at most the value 2?a)16/81b)17/81c)47/243d)46/243Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice X is a binomial variable such that 2 P(X = 2) = P( x = 2) and mean of X is known to be 10/3. What would be the probability that X assumes at most the value 2?a)16/81b)17/81c)47/243d)46/243Correct answer is option 'B'. 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