Final answer:
The question involves solving for missing values in a probability distribution function table and calculating certain probabilities.
Basic principles of discrete and continuous probability distributions are applied to determine the probabilities of specific events.
Step-by-step explanation:
The question asks to complete the probability distribution function table and calculate specific probabilities based on given or missing values in the table. To solve the question, we need to know the basic properties of probability distribution functions for both discrete and continuous cases.
For a discrete probability distribution, all probabilities must sum to 1, and each probability value must be between 0 and 1. For a continuous probability distribution, the total area under the density function over all possible values of x must equal to 1.
For example, if you need to find P(x = 3) in a discrete distribution, you would look at the value provided for when x equals 3. If the distribution were continuous and you were asked for P(x = a specific value) where x is within the range of the distribution, the probability would be 0 because a single point has no area under a continuous curve.
Similarly, if you were asked to find the probability of x being within a certain range, you would calculate the area under the curve, or sum the probabilities in that range for a discrete distribution.
In the case of P(x > 15) for a continuous probability distribution that only goes up to x=15, this probability would be 0 because there is no area under the curve beyond x=15.