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A random variable x follows Binomial distribution with mean 2 and variance 1.6 then the value of p is
- a)1/5
- b)4/5
- c)3/5
- d)none
Correct answer is option 'A'. Can you explain this answer?
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A random variable x follows Binomial distribution with mean 2 and vari...
Binomial Distribution
Binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials. It has two parameters - n (number of trials) and p (probability of success in each trial).
Mean and Variance of Binomial Distribution
The mean (μ) and variance (σ²) of the binomial distribution are given by:
μ = np
σ² = np(1-p)
Given that the mean of x is 2 and the variance is 1.6, we can write:
μ = np = 2
σ² = np(1-p) = 1.6
Solving these equations, we get:
p = μ/n = 2/n
σ² = np(1-p) = 1.6
Substituting the value of p in the second equation, we get:
1.6 = 2/n * (1 - 2/n)
Simplifying this equation, we get:
n² - 5n + 8 = 0
Solving this quadratic equation, we get:
n = 4 or n = 1
Since n is the number of trials, it cannot be 1. Therefore, n = 4.
Substituting the value of n in the expression for p, we get:
p = 2/4 = 1/2
Therefore, the correct option is A) 1/5.
Explanation:
Option A is the correct answer because it corresponds to the value of p = 1/2 - which we obtained from the mean and variance of the binomial distribution. The other options are incorrect because they do not correspond to the calculated value of p.
Binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials. It has two parameters - n (number of trials) and p (probability of success in each trial).
Mean and Variance of Binomial Distribution
The mean (μ) and variance (σ²) of the binomial distribution are given by:
μ = np
σ² = np(1-p)
Given that the mean of x is 2 and the variance is 1.6, we can write:
μ = np = 2
σ² = np(1-p) = 1.6
Solving these equations, we get:
p = μ/n = 2/n
σ² = np(1-p) = 1.6
Substituting the value of p in the second equation, we get:
1.6 = 2/n * (1 - 2/n)
Simplifying this equation, we get:
n² - 5n + 8 = 0
Solving this quadratic equation, we get:
n = 4 or n = 1
Since n is the number of trials, it cannot be 1. Therefore, n = 4.
Substituting the value of n in the expression for p, we get:
p = 2/4 = 1/2
Therefore, the correct option is A) 1/5.
Explanation:
Option A is the correct answer because it corresponds to the value of p = 1/2 - which we obtained from the mean and variance of the binomial distribution. The other options are incorrect because they do not correspond to the calculated value of p.
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Community Answer
A random variable x follows Binomial distribution with mean 2 and vari...
Np=2
npq=1.6
p=1-q
2*q=1.6
q=0.8
p=1-0.8
=0.2=2/10=1/5
npq=1.6
p=1-q
2*q=1.6
q=0.8
p=1-0.8
=0.2=2/10=1/5
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A random variable x follows Binomial distribution with mean 2 and variance 1.6 then the value of p isa)1/5b)4/5c)3/5d)noneCorrect answer is option 'A'. Can you explain this answer?
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