Question

Write the relationship between mean and variance of a Bernoulli distribution

Answer 1

Answer:

The difference between variance Bernoulli distribution

Answer 2

Answer:

The relationship between mean and variance of a Bernoulli distribution

is a binomial variable's variance is always lower than its mean.

Step-by-step explanation:

Bernoulli distribution :

The outcome of the Bernoulli random variable may only be either   or  , making the Bernoulli distribution a discrete probability distribution. The probability of success is $p$, whereas the probability of failure is $1-p$ . A Bernoulli distribution has a mean of $E[X]=p$ and a variance $Var[X]=p.(1-p)$.

We are aware that the mean of the Bernoulli distribution $b(n,p)$ is given by $np$ and variance $=npq$, where $p$ is the probability of success and $q=(1-p)$ is the probability of failure. Therefore   $Variance =q \times( mean )$

Therefore, the mean is greater than variance (p>pq) in Bernoulli distribution .

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