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 the average number of accidents occurring at a particular junction on a highway in a week is 5, then the probability that at most one accident occurs in a particular week is:

In a binomial distribution, if \(n=4\) and \( P(X=0) = \frac{16{81} \), then \( P(X=4) = \)}

Let \(X \sim B(n, p)\) with mean \(\mu\) and variance \(\sigma^2\). If \(\mu = 2\sigma^2\) and \(\mu + \sigma^2 = 3\), then find \(P(X \leq 3)\).

In a binomial distribution, if \(n=4\) and \( P(X=0) = \frac{16}{81} \), then \( P(X=4) = \)

If the average number of accidents occurring at a particular junction on a highway in a week is 5, then the probability that at most one accident occurs in a particular week is:

A random variable \(X\) follows a binomial distribution in which the difference between its mean and variance is 1. If \(2P(x=2) = 3P(x=1)\), then \(n^2 P(x>1)\) is:

If a random variable X follows poison distribution such that 3P(X=1)=P(X=2), then P(X=4) is,

In a city it is found that 10 accidents took place in a span of 50 days. Assuming that the number of accidents follow the Poisson distribution, the probability that there will be 3 or more accidents in a day in that city, 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 \[ e^4\left[1-P(X\gt 2)\right]= \]

If variance of a Poisson distribution is 3, find: \[ P(1<X<4) \]