Question

A property of continuous distributions is that:

a) As with discrete random variables, the probability distribution can be approximated by a smooth curve.
b) Probabilities for continuous variables can be approximated using discrete random variables.
c) Unlike discrete random variables, probabilities can be found using tables.
d) Unlike discrete random variables, the probability that a continuous random variable equals a specific value is zero [P(X = x) = 0].

Answer 1

A property of continuous distributions is that the probability that a continuous random variable equals a specific value is zero. So Option c, d.

Step-by-step explanation:

A property of continuous distributions is that the probability that a continuous random variable equals a specific value is zero, written as P(X = x) = 0. This is because the values of a continuous random variable are uncountable and obtained by measuring, not counting.

Instead, probabilities for continuous variables are found by calculating the probability that the value falls within a particular range. For example, we calculate P(c < x < d), which is the probability that the value of x is between the values c and d.

Unlike discrete random variables, the probability distribution for continuous random variables is represented by a smooth curve called the probability density function (pdf). The area under the curve represents the probability, and the total area under the curve is always one.

So Option c, d.