I have this nifty (and fair) three-sided die. The possible outcomes are S = {1,2
ID: 3130047 • Letter: I
Question
I have this nifty (and fair) three-sided die. The possible outcomes are S = {1,2,3}. Its probability mass function (pmf) is fx(x):={1/3 1/3 1/3 x=1 x=2 x=3 Fill out the distribution table: What is the expected value of the die? What is the variance? What is the probability that a 1 is rolled? What is the probability that a 1 or a 2 is rolled? I roll the die twice, what is the probability that a 1 comes up on both rolls? I roll the die twice, what is the probability that a 1 comes up on cither roll? I roll the die twice, what is the probability that I roll a sum of 6? Given that I rolled a 1 on the first roll, what is the probability that I roll a 1 on the second roll? Are the events "Rolling a 1 on the first roll" and "Rolling two dice that sum to 5" mutually exclusive-?Explanation / Answer
1.
As given,
2.
Consider:
Thus,
E(x) = Expected value = mean = Sum(xP(x)) = 2 [ANSWER]
****************
3.
Var(x) = E(x^2) - E(x)^2 = 0.666666667 [ANSWER]
*********************
4.
As given,
P(1) = 1/3 [ANSWER]
*******************************************
Hi! Please submit the next part as a separate question. That way we can continue helping you! Please indicate which parts are not yet solved when you submit. Thanks!
xi 1 2 3 P(X = xi) 1/3 1/3 1/3