If 2 P(2) = P(3) in a Poisson's distribution, what is the value of Var (X)?

1. Write down the Poisson probability formula:
P(k) = \frac{\lambda^k e^{-\lambda}}{k!}

2. Use the condition \(2 P(2) = P(3)\):
2 \frac{\lambda^2 e^{-\lambda}}{2!} = \frac{\lambda^3 e^{-\lambda}}{3!}

3. Simplify the equation:
\lambda^2 = \frac{\lambda^3}{6}

4. Solve for \(\lambda\):
- Divide both sides by \(\lambda^2\):
1 = \frac{\lambda}{6}
- Multiply both sides by 6:
\lambda = 6

5. For a Poisson distribution, variance Var(X) is \(\lambda\).

Answer is 6.