What distribution would you expect for these scenarios?

[bamboozle]

What sort of distribution (eg binomial, normal..) would you expect each of the following to be? I am trying to get my head around all of these, so any help will be appreciated!

1)the number of goals scored during a football match
2)the height in inches of an individual
3)the number of tosses of a coin before 5 heads are observed
4)the number of heads in 20 tosses of a coin
5)the number of deaths by suicide in a large town in a year

Could you help me to estimate the parameters of the distribution, or identify some of the characteristics to let me know why?

thanx

 

[NateTG]

http://mathworld.wolfram.com/ContinuousDistribution.html
http://mathworld.wolfram.com/DiscreteDistribution.html

has more information about distributions.

Binomial or normal distributions typically occur when the results of a large number of independant events are tallied. The traditional example is coin flips, but the events need not be identical.

Normal and Binomial distributions are essentially the same, but binomial distributions are for discrete of possible end states while normal distributions are for a continuum of results.

Uniform distributions typically occur when there is a single event with may different possible results, or a sequence of events in which the order matters.

Exponential distributions typically occur when a series of events that directly depend on the previous result.

So, let's take a look at your examples:

1. (This one is tricky) The number of goals in a football game depends on many independant things (regardless of order), and the list of possible resutls is discrete.

2. The height of a person depends on many different independant things, and has results over a continuum.

3. Each coin flip depends on the previous coin flips.

4. This is the total of a number of independant events.

5. This is the total of a number of independant events. (Discounting the change in the size of the town.)

 

[tacman]

1) For the number of goals scored during a football match, we would expect a binomial distribution. This is because there are only two possible outcomes (goal or no goal) and each goal scored is independent of the others. The parameters for this distribution would be the probability of scoring a goal (which may vary depending on the teams playing) and the number of trials (matches).

2) The height in inches of an individual would likely follow a normal distribution. This is because it is a continuous variable and the majority of people fall within a certain range of heights. The parameters for this distribution would be the mean and standard deviation of the heights in the population.

3) The number of tosses of a coin before 5 heads are observed would follow a negative binomial distribution. This is because the number of trials (tosses) is fixed and we are interested in the number of successes (heads) before a certain number is reached. The parameters for this distribution would be the number of successes (5) and the probability of success (0.5 for a fair coin).

4) The number of heads in 20 tosses of a coin would also follow a binomial distribution, similar to the first scenario. The only difference is that the number of trials (tosses) is fixed at 20.

5) The number of deaths by suicide in a large town in a year would likely follow a Poisson distribution. This is because it is a count variable and the events (deaths by suicide) occur randomly and independently of each other. The parameters for this distribution would be the mean, which can be estimated by the average number of deaths by suicide in the town in previous years.