Question

Please suggest two different types of random variables from your daily life. Specify the type of the random variables you are proposing. Explain the measurement unit and frequency of the variables. Elaborate on the probability distribution of those random variables. Propose a visual tool for presentation of those random variables.

Answer 1

Answer:

There are two types of random variables occurs in our dialy life.

There are  discrete and continuous. Let's talk about discrete random variable.

(1) Discrete Random Variables::

A discrete random variable is one which may take on only a countable number of distinct values such as 0,1,2,3,4,........ Discrete random variables are usually (but not necessarily) counts. If a random variable can take only a finite number of distinct values, then it must be discrete. Examples of discrete random variables include the number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor's surgery, the number of defective light bulbs in a box of ten.

The probability distribution of a discrete random variable is a list of probabilities associated with each of its possible values. It is also sometimes called the probability function or the probability mass function.

Suppose a random variable X may take k different values, with the probability that X = x_i defined to be P(X = x_i) = p_i. The probabilities p_i must satisfy the following:

1: 0 < p_i< 1 for each i

2: p₁ + p₂ + ... + p_k = 1.

Now the other random variable is Continuous Random Variable.

(2 ) Continuous Random Variable::

A continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements. Examples include height, weight, the amount of sugar in an orange, the time required to run a mile.

A continuous random variable is not defined at specific values. Instead, it is defined over an interval of values, and is represented by the area under a curve (in advanced mathematics this is known as an integral). The probability of observing any single value is equal to 0, since the number of values which may be assumed by the random variable is infinite.

Suppose a random variable X may take all values over an interval of real numbers. Then the probability that X is in the set of outcomes A, P(A), is defined to be the area above A and under a curve.

The curve, which represents function p(x), must satisfy the following:

1: The curve has no negative values (p(x) > 0 for all x)

2: The total area under the curve is equal to 1.

The visualisation of random variables are based on the context of time. If the given is discrete on time it is said to be discrete random variable. If it is continuous then it is said to be continuous random variable.

I propose continuous random variable becuase it helps in understanding the context very clearly when compared with discrete random variable.

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