A variable that follows a discrete distribution can take only particular values. For example, counts follow discrete distributions. There is a particular probability that the variable equals each value. With a continuous distribution, the probability that the variables take anyparticular value is 0 because there are an infinite number of values. The variable can take any value in the interval over which the probability distribution is defined.
How is the expected outcome determined in a discrete distribution?
The expected value of a discrete distribution is the summation of the value times the probability. The expected value of a continuous variable is the area under theprobability density curve.
Write two brief scenarios: one that illustrates a discrete distribution and one that illustrates a continuous distribution.
Suppose you were counting the number of accidents at an intersection. This variable is discrete. That is, it can only take values like 0, 1, 2, 3, 4, etc.
A continuous variable might be the time between accidents at an intersection. In this case,any time interval could be obtained.
Respond to your classmates by identifying the discrete and continuous distributions. Elaborate on the scenarios by providing more detail about what the distribution might look like? Will it be a normal distribution? In some cases, the scenario may not include the details necessary to describe the distribution. Provide these details yourself and then describethe distribution.
If you'll provide their responses, I'd be happy to respond to them.
Customer replied 1040 days and 2 hours ago.
Thank you for your help. Here are some posting of the classmates:
1. The similarities between discrete and a continuous probability distribution are that both variables are random.
The differences between discrete and a continuous probabilitydistribution are that discrete probability is for a set group of numbers while continuous probability can be any number at all within a given range. In a discrete probability 0 isn't a possibility while in a continuous probability 0 can be a possibility. Discrete probabilities have to increase while continuous do not have to increase.
The expected outcome determined in a discrete distribution is ifgiven a specific range of numbers; for instance 1 - 10, then the answer will be between 1 and 10. (This is a guess!)
A discrete distribution scenario would be if people at a job had to weigh between 150-200 pounds. No person employed at this job could weigh anything more or less than 150-200 pounds. More discrete examples could include the number of students within a class and the number ofchildren in a family to name a few.
A continuous distribution would be like flipping a coin. We could get anything from 0 to infinity. We could not get any number that wasn't a whole number such as 2.5 because there is no such thing as a half flip. Another example is the distance that each student travels to get to school everyday, the time it takes every person in one building to arrive at work or thelength of a phone call.
"A probability distribution is called discrete if its cumulative distribution function only increases in jumps. More precisely, a probability distribution is discrete if there is a finite or countable set whose probability is 1.
For many familiar discrete distributions, the set of possible values is topologically discrete in the sense that all its points areisolated points. But, there are discrete distributions for which this countable set is dense on the real line.
"Discrete distributions are characterized by a probability mass function, p such that
Continuous probability distribution
Main article: Continuous probability distribution
By one convention, a probability distribution is called continuous if its cumulative distribution function is...