Moderate -0.3 This question requires understanding that independent Poisson processes sum to another Poisson distribution, then converting rates to a common time period (4 weeks) and calculating E(T) and Var(T). While it involves multiple steps and rate conversion, it's a standard application of Poisson properties with straightforward arithmetic, making it slightly easier than average.
1 At a particular hospital, admissions of patients as a result of visits to the Accident and Emergency Department occur randomly at a uniform average rate of 0.75 per day. Independently, admissions that result from G.P. referrals occur randomly at a uniform average rate of 6.4 per week. The total number of admissions from these two causes over a randomly chosen period of four weeks is denoted by \(T\). State the distribution of \(T\) and obtain its expectation and variance.
1 At a particular hospital, admissions of patients as a result of visits to the Accident and Emergency Department occur randomly at a uniform average rate of 0.75 per day. Independently, admissions that result from G.P. referrals occur randomly at a uniform average rate of 6.4 per week. The total number of admissions from these two causes over a randomly chosen period of four weeks is denoted by $T$. State the distribution of $T$ and obtain its expectation and variance.
\hfill \mbox{\textit{OCR S3 2009 Q1 [4]}}