Question
Let X be a random variable that records the outcome of a dice toss. The probability distribution for X is as follows:
Outcome: 1, 2, 3, 4, 5, 6
Probability: 1/6, 1/6, 1/6, 1/6, 1/6, 1/6
Suppose now that we toss two dice. X1 records the outcome of the first toss, and X2 records the outcome of the second toss. We are interested in the sum of the two dice tosses,
Y= X1+ X2.
Do you think that X1and X2 are independent random variables?
Outcome: 1, 2, 3, 4, 5, 6
Probability: 1/6, 1/6, 1/6, 1/6, 1/6, 1/6
Suppose now that we toss two dice. X1 records the outcome of the first toss, and X2 records the outcome of the second toss. We are interested in the sum of the two dice tosses,
Y= X1+ X2.
Do you think that X1and X2 are independent random variables?
Answers
GPT 3.5
Yes, X1 and X2 are independent random variables. The outcome of one dice toss does not affect the outcome of the other dice toss. Each toss is independent and has the same probability distribution, making X1 and X2 independent.