Consider the discrete random variable X with values coming from rolling a modied
ID: 3129595 • Letter: C
Question
Consider the discrete random variable X with values coming from rolling a modied exploding d6, described as follows: Roll a standard 6-sided die. If a 1,2,3,4, or 5 is rolled, then the rolled number (1,2,3,4, or 5) is the value. If a 6 is rolled, you subtract 1 and reroll the die with the same rules, adding the value of successive rolls to your total. This process can continue indenitely. For example, let’s say I roll and the die comes up 6, I subtract one from my rst roll (so now I am at 5) and reroll the die, which comes up 4 on the second roll. I add this to my rst roll to obtain 9. What is E(X)? Justify your answer.
Explanation / Answer
Consider the discrete random variable X with values coming from rolling a modied exploding d6, described as follows: Roll a standard 6-sided die. If a 1,2,3,4, or 5 is rolled, then the rolled number (1,2,3,4, or 5) is the value. If a 6 is rolled, you subtract 1 and reroll the die with the same rules, adding the value of successive rolls to your total. This process can continue indenitely. For example, let’s say I roll and the die comes up 6, I subtract one from my rst roll (so now I am at 5) and reroll the die, which comes up 4 on the second roll. I add this to my rst roll to obtain 9. What is E(X)? Justify your answer.
Solution:
For the six sided die, if the outputs 1, 2, 3, 4 and 5 are appeared we count them as same and while output 6 is comes, then we count it as 6 – 1 = 5. The probability distribution and the expected value are given as below:
E(X) = XP(X)
Outcome X
Probability P(X)
XP(X)
1
0.1667
0.1667
2
0.1667
0.3333
3
0.1667
0.5000
4
0.1667
0.6667
5
0.3333
1.6667
Total
1.0000
E(X) = 3.3333
Expected value = E(X) = 3.3333
Outcome X
Probability P(X)
XP(X)
1
0.1667
0.1667
2
0.1667
0.3333
3
0.1667
0.5000
4
0.1667
0.6667
5
0.3333
1.6667
Total
1.0000
E(X) = 3.3333