Question

Consider the experiment of tossing a pair of dice. Let X be the outcome on the first die, and let Y be the outcome on the second die. What is the probability distribution of X+Y?

a) Binomial distribution
b) Uniform distribution
c) Normal distribution
d) Poisson distribution

Answer 1

The probability distribution of X+Y is a uniform distribution.

Step-by-step explanation:

The probability distribution of X+Y can be represented by a uniform distribution.

To find the probability distribution of X+Y, we need to find all the possible outcomes of X+Y and their corresponding probabilities. Since the outcomes of X and Y are from 1 to 6, the possible outcomes of X+Y range from 2 to 12. Each outcome has a probability of 1/36, except for the outcomes of 7 and 13, which have a probability of 1/18.

Therefore, the probability distribution of X+Y is:

1. X+Y=2: probability=1/36
2. X+Y=3: probability=2/36
3. X+Y=4: probability=3/36
4. X+Y=5: probability=4/36
5. X+Y=6: probability=5/36
6. X+Y=7: probability=6/36
7. X+Y=8: probability=5/36
8. X+Y=9: probability=4/36
9. X+Y=10: probability=3/36
10. X+Y=11: probability=2/36
11. X+Y=12: probability=1/36