4.17 Poisson distributionIB Maths: Applications and Interpretation HL: Flashcards

What these 12 flashcards ask

What are the conditions for a Poisson model?
Write down P(X=r) for X\simPo(\lambda).
Mean and variance of Po(\lambda)?
A rate of 4 per hour: what is \lambda for 30 minutes?
X\simPo(\lambda), Y\simPo(\mu) independent: distribution of X+Y?
How do you find P(X\ge r) on the GDC?
How do you find P(X3)?
Name a situation where Poisson events are not independent.
How do you tell binomial from Poisson?
When is the normal distribution the right model?
Is X-Y Poisson when X and Y are independent Poisson variables?
Do you need to prove that the mean and variance of Po(\lambda) are \lambda?

Exam questions on 4.17 Poisson distribution

Calls to a school office arrive independently at a uniform average rate of $4$ calls per hour. Let $N$ be the number of calls in a one-hour period.
Find the probability that at least $2$ calls arrive in a $30$ -minute period.2 marks
Flaws occur in rolls of fabric independently of each other, at a uniform average rate of $0.8$ per square metre in fabric X and $1.5$ per square metre in fabric Y.
Two square metres of fabric X and one square metre of fabric Y are inspected. Use your GDC to find the probability that more than $3$ flaws are found in total.2 marks
Patients arrive at the emergency department of a hospital during the night at an average rate of $5$ per hour. Let $X$ be the number of patients who arrive in a one-hour period during the night.
State two conditions needed for $X$ to be modelled by a Poisson distribution, and give one reason why arrivals at an emergency department might not satisfy a condition.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).