Final answer:
To finalize the discrete probability distribution, we calculate the missing value for P(X = 20) and conclude it is 0.37. We then determine the probabilities where X is positive, greater than -23, and less than 17 to be 0.47, 0.55, and 0.63 respectively.
Step-by-step explanation:
To complete the discrete probability distribution, we need to find the missing probability P(X = 20). Since all probabilities must sum to 1, we can calculate it as 1 - (0.45 + 0.08 + 0.10) = 0.37. Therefore, P(X = 20) = 0.37.
The probability that the random variable X is positive is the sum of the probabilities for all positive values of X, which are 10 and 20. Hence, the probability is P(X = 10) + P(X = 20) = 0.10 + 0.37 = 0.47.
The probability that the random variable X is greater than -23 only excludes the value -25, so we sum the probabilities of the remaining values: 0.08 + 0.10 + 0.37 = 0.55.
To find the probability that X is less than 17, we include all values of X that are less than 17, which are -25, -15, and 10. We sum their probabilities: 0.45 + 0.08 + 0.10 = 0.63.