University of Phoenix Discrete and Continuous Random Variables Paper

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Business Finance

University of Phoenix

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Answer the following IN YOUR OWN WORDS. Respond to each of the following in a minimum of 175 words each. It will be run thru a plagiarism checker, thanks.

Many business activities generate data that can be thought of as random. An example described in the textbook is the servicing of cars at an oil change shop. Each car entering the shop can be considered an experiment with random outcomes. A variable of interest in this experiment could be the amount of time necessary to service the car. Service time will vary randomly with each car.

We can often capture the most relevant characteristics of a stochastic process with a simple probability distribution model. We can then analyze the model to make predictions and drive decisions. For instance, we could estimate the number of technicians the oil change shop needs to service demand on a Saturday afternoon. Discuss the following:

1.What is a random variable?

2.How would you differentiate a discrete from a continuous random variable?

A laptop manufacturing company has implemented a 2-step process to test the quality of each production batch. In the first step, a technician randomly selects 15 laptops from the batch and determines whether they meet specifications. The batch is considered acceptable provided no more than 1 laptop fails to meet specifications. Otherwise, the entire batch must be tested in the second step. Historical data shows that 95% of the laptops produced adhere to specifications. Discuss the following:

1.What are the 4 characteristics of a binomial experiment?

2.Can we use a binomial distribution to model this process?

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DISCRETE AND CONTINOUS RANDOM VARIABLES

Discrete and Continuous Random Variables
Name
Institution

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DISCRETE AND CONTINOUS RANDOM VARIABLES

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Discrete and Continuous Random Variables
What is a random variable?
According to Bas, (2019) a random variable, is any variable in which its values depend
only on outcomes of a random experiment. In this scenario, the values of the variables are not
fixed but absolutely takes values of all possible outcome values of the experiment.
How would you differentiate a discrete from a continuous random variable?
For example, let’s say the values of X are countable then X then we can conclude that X
is a discrete random variable. On the other hand, when the values of sample X are not countable
and they take values on the real line then X is a continuous random variable (Bas, 2019).
What are the 4 characteristics of a binomial experiment?
i.

There is always a fixed number of repeated trials in a binomial distribution.

ii.

There are only two possible outcomes.

iii.

The probability of success, p, is constant in each trial.

iv.

All the trials are independent.

Can we use a binomial distribution to model this process?
Basing our explanation from the characteristics of binomial experiment, the model
satisfies all the assumptions as follows; the sample size (n) is always fixed and in this case, the
value of n = 15 satisfies the requirement. There are only two outcomes for the laptops to meet the
specifications either succeed or fail to meet the requirements thus, satis...

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