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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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