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STA1501 Assignment 3 SOLUTIONS 2023 [Unique No.: 827246]

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  • STA1501 - Descriptive Statistics And Probability
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  • University Of South Africa (Unisa)

Complete solutions with detailed explanations for each question. Guaranteed to get you very good marks on your assignment, plus you will have valuable material for study/revision purposes. Contact us should you have any queries. please remember to leave a review if you find this document helpful:)

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  • June 5, 2023
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  • sta1501 assignment 3

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  • University of South Africa (Unisa)
  • STA1501 - Descriptive Statistics And Probability
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STA1501


Assignment 3
2023


Unique No.: 827246



Due date: 12 June 2023




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State whether the following statements are true or false.

QUESTION 1 [1 mark]

A random variable in a probability distribution can be either of a discrete type or of a continuous
type.

True. A random variable in a probability distribution can indeed be either of a discrete type or of a
continuous type.

Discrete random variables take on a finite or countably infinite set of possible values. Examples
include the number of heads in a series of coin tosses or the number of students in a class.

On the other hand, continuous random variables can take on any value within a certain range or
interval. They are typically associated with measurements or quantities that can have infinitely
many possible values. Examples include the height of a person, the time it takes for a process to
complete, or the temperature of a room.

In summary, random variables can be classified as either discrete or continuous, depending on the
nature of the values they can take in a probability distribution.



QUESTION 2 [1 mark]

The use of an appropriate probability distribution will enable you to determine the probability that a
discrete random variable will have a given value (integer) or a value in a given range.

True. The use of an appropriate probability distribution allows you to determine the probability
that a discrete random variable will have a specific value or fall within a given range.

Probability distributions for discrete random variables, such as the binomial distribution, Poisson
distribution, or geometric distribution, provide a mathematical framework for quantifying the
likelihood of different outcomes. These distributions assign probabilities to each possible value
that the random variable can take.

To determine the probability that a discrete random variable will have a specific value, you can
directly calculate the probability mass function (PMF) for that value. The PMF gives the probability
of each possible outcome.

Similarly, to determine the probability that a discrete random variable falls within a given range,
you can sum the probabilities of all the values in that range using the PMF. This provides the
cumulative probability or the probability of observing a value within the specified range.

Therefore, by utilizing the appropriate probability distribution, you can compute the probabilities
associated with specific values or ranges for a discrete random variable.




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