Exponential distribution model, pdf and CDFAQA A-Level Further Maths: Mind map

Exam questions on Exponential distribution model, pdf and CDF

1. Calls to a helpline arrive at random, independently of each other, at a constant average rate of 3 per hour. The time, $X$ hours, between successive calls is modelled by an exponential distribution with probability density function $f(x)=3e^{-3x}$ for $x\ge0$.
   Find the probability that the time between two successive calls is between 12 minutes and 30 minutes.2 marks
2. The lifetime, $T$ years, of a certain type of component is modelled by a continuous random variable with cumulative distribution function $F(t)=1-e^{-0.2t}$ for $t\ge0$.
   The pdf of $T$ is $f(t)=0.2e^{-0.2t}$ for $t\ge0$. Use integration to find the exact probability that a component fails within 5 years.2 marks
3. The time, $X$ minutes, between successive arrivals at a supermarket checkout is modelled by an exponential distribution with parameter $\lambda$, where $\lambda>0$ is a constant. It is known that $\mathrm{P}(X>2)=0.3$.
   Find the value of $\lambda$.3 marks