Final answer:
A probability distribution is a discrete PDF that represents the likelihood of each value of a random variable. It can be graphed, and the mean and standard deviation can be calculated.
Step-by-step explanation:
X takes on the values: 0, 1, 2, 3, 4, 5. This is a discrete probability distribution (PDF) because we can count the number of values of X. Each P(X) is between zero and one and the sum of the probabilities is one.
a. Sketching a graph: To sketch the graph of the probability distribution of X, we plot the X values on the x-axis and the corresponding probabilities on the y-axis.
b. Calculating the mean: The mean of X, also known as the expected value, is calculated by multiplying each X value by its corresponding probability and summing the products.
c. Calculating the standard deviation: The standard deviation of X can be calculated using the formula: square root of the sum of the squared differences between each X value and the mean, multiplied by their corresponding probabilities.