Let X be a binomially distributed random variable with mean 2 and variance 4/3. Tabulate the probability distribution of X.

Question

I'm practicing for a test that I'm writing tomorrow and one of the past questions was:

Let X be a binomially distributed random variable with mean 2 and variance 4/3. Tabulate the probability distribution of X.

For Binomial Distribution, we learnt that the mean (µ) = np, where n is the sample and p is probability of success and the variance σ^2 = np(1 - p).

The only thing I could think of doing is:

2 = np and 4/3 = np(1 - p)

4/3 = 2 (1 - p)

1/3 = p

2 = n(1/3)

n = 6

This is as far as I can get.

Answer 1

Guide:

Great, you have solved the parameters.

Now, you just have to use the formula

$$Pr(X=i) = \begin{cases} \binom{6}{i}\left( \frac13 \right)^i \left( \frac23 \right)^{6-i}& i \in \{ 0, \ldots, 6\}\\ 0 & \text{Otherwise}\end{cases}$$