List of top Mathematics Questions on Poisson distribution

The integral \( \int \frac{x^5}{\sqrt{1+x^3}} \, dx \) is equal to:

If the probability that a person suffers a bad reaction from an injection is $0.001$, then the probability that out of $2000$ individuals, exactly $3$ will suffer a bad reaction is:

If \(X\) is a Poisson random variable with mean \(3\), then \[ P(|X-3|\lt 2) = \] is equal to:

If \(3\) is the variance of Poisson distribution, then \[ P(1\lt x\lt 4)= \] is:

For a Poisson distribution, if mean \(=\ell\), variance \(=m\) and \[ \ell+m=8, \] then \[ e^4\left[1-P(X\gt 2)\right]= \]