Final answer:
The probability of X being equal to 3 is 0.05 and the probability of Y being equal to 20 is also 0.05. The probability mass function of X and Y is uniform, with a probability of 1/20 for each value. The cumulative distribution function of X and Y can be represented as step functions.
Step-by-step explanation:
a. The probability of X being equal to 3 can be calculated by dividing the number of favorable outcomes (in this case, the number 3) by the total number of possible outcomes (20). So, Pr(X=3) = 1/20 = 0.05.
b. The probability of Y being equal to 20 can be calculated by dividing the number of favorable outcomes (in this case, the number 19) by the total number of possible outcomes (20). So, Pr(Y=20) = 1/20 = 0.05.
c. The probability mass function of X is a function that assigns probabilities to each possible value of X. In this case, X can take on any value from 1 to 20. Since every value has an equal probability of being drawn, the probability mass function is uniform, with a probability of 1/20 for each value of X.
d. The probability mass function of Y is also uniform, with a probability of 1/20 for each value of Y from 1 to 19.
e. The cumulative distribution function of X gives the probability that X is less than or equal to a certain value. In this case, since the probability of each value of X is 1/20, the cumulative distribution function of X can be represented as a step function, with a step of 1/20 at each value of X from 1 to 20.
f. The cumulative distribution function of Y can be represented as a step function as well. It starts at 0 for Y=1 and increases by 1/20 at each value of Y from 1 to 19.