Final answer:
The cumulative distribution function (CDF) of a random variable gives the probability that X is less than or equal to x. To calculate specific probabilities, evaluate the CDF at the given value or use the properties of the CDF.
Step-by-step explanation:
The cumulative distribution function (CDF) of a random variable X is defined as P(X ≤ x), which gives the probability that X is less than or equal to x. To compute the probabilities (a) P{X ≤ 10}, (b) P{X ≥ -7}, and (c) PX, we can use the properties of the CDF.
(a) P{X ≤ 10} is the probability that X is less than or equal to 10. We can find this probability by evaluating the CDF at x = 10.
(b) P{X ≥ -7} is the probability that X is greater than or equal to -7. We can find this probability by subtracting P{X < -7} from 1.
(c) PX is the probability that the absolute value of X is less than or equal to a certain value. We can find this probability by finding the difference between P{X ≤ x} and P{X ≤ -x}.