Q52 What is a probability density function and how is it relevant to the determination of...

Q52 What is a probability density function and how is it relevant to the determination of probabilities associated with a continuous random variable? [3 Marks]

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The probability density function (PDF) is used for a continuous random variable rather than a discrete variable. We know that in a continuous random variable, there are infinite number of points, hence the absolute value of the likelihood that the the function will take a particular value of x will be 0. PDF is used where it tells us the relative likelihood of the point OR how much more likely that the function will take on a given value.

PDF can be used to find out the probability that the random variable will fall in a particular range of values. This can be found by integrating the pdf over the range which is the same as finding the area under the density function graph (within the range of-course).

The probability density function is non-negative because the probability cannot be negative, and the integral over the entire range/space is always equal to one.

orchestra answered 2 years ago

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