if the sum of the mean and variance of binomial distribution of 5trails is 4.8 ,find the corresponding pmf of the distribution

The problem states that we have a binomial distribution with n=5 trials. The sum of the mean and variance of this distribution is given as 4.8.

The mean (μ) and variance (σ^2) of a binomial distribution are given by:

μ = np σ^2 = np(1-p)

where: n = number of trials p = probability of success on each trial

Given that μ + σ^2 = 4.8, we can substitute the formulas for mean and variance into this equation to get:

np + np(1-p) = 4.8

Solving this equation for p gives us the probability of success on each trial. Once we have p, we can use the formula for the probability mass function (pmf) of a binomial distribution to find the pmf:

P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))

where: P(X=k) = probability of k successes in n trials C(n, k) = number of combinations of n items taken k at a time p = probability of success on each trial n = number of trials k = number of successes

This will give us the pmf of the distribution.