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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?
Most Upvoted Answer
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.
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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
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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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