Final answer:
To determine the probability that the random variable X falls within a specific range based on a given probability density function, you need to find the area under the curve between the two values. This can be done by calculating the cumulative probability at each of these values using the given probability density function.
Step-by-step explanation:
In order to determine the probability that the random variable X falls within the range 0.18 to 1.42 based on a given probability density function, we need to find the area under the curve between these two values. This can be done by calculating the cumulative probability at each of these values using the given probability density function.
Let's assume the probability density function is f(x) and the cumulative distribution function is F(x). We can then calculate the probability as P(0.18 < X < 1.42) = F(1.42) - F(0.18).
By evaluating these values using a calculator, computer, or a probability table, you can find the exact probability.