Final answer:
The lifetime of an electronic component, which is a continuous random variable, can be modeled by an exponential distribution with a probability density function (pdf) as f(x) = me-mx, where m is the decay parameter and x is the time.
Step-by-step explanation:
The probability density function (pdf) for a continuous random variable is a fundamental concept in probability and statistics, which describes the likelihood of a random variable's value falling within a particular range. For a variable related to the lifetime of electronic components, the pdf is particularly important when considering components with lifetimes modeled by an exponential distribution. This distribution is often used to model the time between events, such as the expected lifetime of certain products like car batteries or electronic devices. For an electronic component with a lifetime following an exponential distribution, if the mean lifetime is provided by μ (mu), then the probability density function would be given by f(x) = me-mx, where m is the decay parameter and x is the time. The total area under the curve of the pdf equals 1, representing the certainty that the lifetime will take some positive value. Additionally, the integral from a to b of the pdf describes the probability P(a < x < b), signifying the chance that the lifetime will fall within that range.