Let the p.m.f. ( probability mass function ) of random variable x be
`P(x) = (4/x)(5/9)^(x)(4/x)^(4-x), x = 0, 1, 2, 3, 4`
= 0 , otherwise
Find E(x) and Var.(x)

Explanation

To find the expected value \( E(X) \) and variance \( Var(X) \) of the given probability mass function (PMF) of the random variable \( X \), we will follow these steps:

### Step 1: Identify the parameters of the PMF
The given PMF is:
\[ P(X = x) = \binom{4}{x} \left( \frac{5}{9} \right)^x \left( \frac{4}{9} \right)^{4-x}, \quad x = 0, 1, 2, 3, 4 \]
This resembles the binomial distribution \( P(X = x) = \binom{n}{x} p^x (1-p)^{n-x} \) where:
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