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Let X be a random variable that follows Binomial distribution with expectation E(X) = 7 and variance V(X) = 6. Then the probability of success p is
- a)6 / 7
- b)36 / 49
- c)1 / 7
- d)1 / 49
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Let X be a random variable that follows Binomial distribution with exp...
Concept:
Binomial distribution: If a random variable X has binomial distribution as B (n, p) with n and p as parameters, then the probability of random variable is given as:
Where, n is number of observations or trials , p is the probability of success & (1 - p) or q is probability of failure.
Properties:
- Mean of the distribution (μX) = n × p
- The variance (σ2x) = n × p × (1 - p)
- Standard deviation (σx) = √{np(1 - p)}
- Expectation, E(X) = np
- 1 - p = q
Calculation:
Given,
Expectation E(X) = 7 = np .........(1)
Variance = 6 = npq .........(2)
From equation (1) & (2)
q = 6 / 7
∴ p = 1 / 7
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Let X be a random variable that follows Binomial distribution with exp...
Given Information:
- Expectation (Mean), E(X) = 7
- Variance, V(X) = 6
Formulae:
- Expectation (Mean) of a binomial distribution: E(X) = np
- Variance of a binomial distribution: V(X) = np(1-p)
Solution:
- From the given information, we have E(X) = 7 and V(X) = 6
- Using the formula for expectation of a binomial distribution, E(X) = np, we get:
7 = n * p ...(1)
- Using the formula for variance of a binomial distribution, V(X) = np(1-p), we get:
6 = n * p * (1-p)
6 = np - np^2
6 = 7p - 7p^2 [Substituting the value of np from equation (1)]
0 = 7p^2 - 7p + 6
0 = 7p^2 - 6p - p + 6
0 = 7p(p-1) - 1(p-1)
0 = (7p-1)(p-1)
- Solving the above equation, we get p = 1/7 or p = 1
- Since probability of success is given by p, the correct answer is option 'C': 1/7.
- Expectation (Mean), E(X) = 7
- Variance, V(X) = 6
Formulae:
- Expectation (Mean) of a binomial distribution: E(X) = np
- Variance of a binomial distribution: V(X) = np(1-p)
Solution:
- From the given information, we have E(X) = 7 and V(X) = 6
- Using the formula for expectation of a binomial distribution, E(X) = np, we get:
7 = n * p ...(1)
- Using the formula for variance of a binomial distribution, V(X) = np(1-p), we get:
6 = n * p * (1-p)
6 = np - np^2
6 = 7p - 7p^2 [Substituting the value of np from equation (1)]
0 = 7p^2 - 7p + 6
0 = 7p^2 - 6p - p + 6
0 = 7p(p-1) - 1(p-1)
0 = (7p-1)(p-1)
- Solving the above equation, we get p = 1/7 or p = 1
- Since probability of success is given by p, the correct answer is option 'C': 1/7.
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Let X be a random variable that follows Binomial distribution with expectation E(X) = 7 and variance V(X) = 6. Then the probability of success p isa)6 / 7b)36 / 49c)1 / 7d)1 / 49Correct answer is option 'C'. Can you explain this answer?
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Let X be a random variable that follows Binomial distribution with expectation E(X) = 7 and variance V(X) = 6. Then the probability of success p isa)6 / 7b)36 / 49c)1 / 7d)1 / 49Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Let X be a random variable that follows Binomial distribution with expectation E(X) = 7 and variance V(X) = 6. Then the probability of success p isa)6 / 7b)36 / 49c)1 / 7d)1 / 49Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let X be a random variable that follows Binomial distribution with expectation E(X) = 7 and variance V(X) = 6. Then the probability of success p isa)6 / 7b)36 / 49c)1 / 7d)1 / 49Correct answer is option 'C'. Can you explain this answer?.
Let X be a random variable that follows Binomial distribution with expectation E(X) = 7 and variance V(X) = 6. Then the probability of success p isa)6 / 7b)36 / 49c)1 / 7d)1 / 49Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Let X be a random variable that follows Binomial distribution with expectation E(X) = 7 and variance V(X) = 6. Then the probability of success p isa)6 / 7b)36 / 49c)1 / 7d)1 / 49Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let X be a random variable that follows Binomial distribution with expectation E(X) = 7 and variance V(X) = 6. Then the probability of success p isa)6 / 7b)36 / 49c)1 / 7d)1 / 49Correct answer is option 'C'. Can you explain this answer?.
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