Further Mathematics 7367: Exponential Distribution Topical Past Paper Questions

The random variable T has an exponential distribution with mean 2 Find P(T ≤ 1.4) Circle your answer. [1 mark] e^{-2.8} e^{-0.7} 1 - e^{-0.7} 1 - e^{-2.8}

The time, T days, between rain showers in a city in autumn can be modelled by an exponential distribution with mean 1.25 Find the distribution of the number of rain showers per day in the city. Tick (✓) one box. [1 mark] $$ \left(\begin{array}{c} \scriptstyle x=1 \\ 3 \times 4 =…

The random variable $X$ has an exponential distribution with parameter $\lambda$ Prove that $E(X) = \frac{1}{\lambda}$ [4 marks] (b) $ \mathrm{Prove~that~Var}(X)=\frac{1}{\lambda^2} $ [7 marks]