NIMCET 2010 — Mathematics PYQ

Solution

1. Understand the Formula

The probability mass function for a Poisson distribution with parameter $\lambda$ (the mean) is:

2. Find the value of $\lambda$

We are given the condition:

Substitute the formula into the equation:

Cancel $e^{-\lambda }$ and ${\lambda }^3$ from both sides:

3. Find the value of $k$

We are given the second relationship:

Substitute the formula with $\lambda =16$:

Cancel $e^{-16}$ and $16^5$ from both sides:

Now, solve for $k$:

Simplify the fraction by dividing by 2:

Correct Option:

The correct option is (b) $\frac{21}{128}$.