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

Guide:

Great, you have solved the parameters.

Now, you just have to use the formula

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