Find the probability that no particle is emitted in 5 minutes the time in minutes for emission of a radioactive particle is a random variable with density f(x)=λ[e^(-λx)] for x>0.the median time for an emission is 2 minutes .Find the probability that no particle is emitted in 5 minutes f(x)=λ[e^(-λx)]. If the λ is 2??

For the exponential probability density equation, $f(x)=\lambda \mathsf e^{-\lambda x}$, the parameter $\lambda$ is known as the rate parameter. The _mean_ is then $\lambda^{-1}$, _however_ what you have is the **median**.

The median $m$ is defined as: $\;\mathbb P(X > m) = \frac 1 2$.

And for any time, $t$ we have $\;\mathbb P(X > t) = \displaystyle{\int}_t^\infty f(x)\operatorname d x$

So, you have been given $m=2$ and wish to find $\mathbb P(X > 5)$.