Final answer:
To find the value of c that makes f(x) a probability density function, we need to satisfy the conditions of a PDF. The probability of any single value is zero, and the total area under the curve is one. To determine the value of c, we can use various methods such as geometry, formulas, technology, or probability tables to find the desired area between c and another value d that represents the probability.
Step-by-step explanation:
A probability density function (PDF) describes the probabilities for continuous random variables. The area under the PDF curve between two points represents the probability that the variable falls between those two values. In this case, we need to find the value of c such that f(x) is a PDF.
- The PDF satisfies the condition that the probability of any single value is zero, so P(x = c) = 0.
- To be a PDF, the total area under the curve must be one, so the area between the curve and the x-axis must equal the probability. Therefore, we have P(c < x < d) = 1.
- Using the given information, we can use geometry, formulas, technology, or probability tables to find the area between c and d that represents the desired probability.
- Remember that for a continuous random variable, the probability that the value of x is between two values c and d is represented as P(c < x < d).