Suppose there are two football teams A and B. In recent matches Team A has a mean of 1 goal per match and Team B has a mean of 2 goals per match. Suppose that the probability of the number of goals scored by a team obeys a Poisson Distribution In the following questions, give the reasoning behind your answers. You can express some answers in terms of logarithms.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
QUESTION 3
Suppose there are two football teams A and B. In recent matches Team A has a mean of 1 goal per match and Team B has a mean of 2 goals per match.
Suppose that the
In the following questions, give the reasoning behind your answers. You can express some answers in terms of logarithms.
Q 3(a)
What is the probability that A beats B by 1 goal? You can give your answer to 2 decimal places.
Q 3(b)
If the two teams play each other repeatedly, what is the probability of there being at least 5 matches before A beats B by 1 goal?
Q 3(c)
In a particular match what is the probability of two goals within the first 20 minutes?
Q 3(d)
What is the second most probable score line?
Q 3(e)
In a particular match, over how long a time period would the probability of exactly one goal be 20%?
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