109k views
4 votes
The following table shows the probability of rolling the numbers 1 through 7 on a fair seven-sided die.

X 1 2 3 4 5 6 7
P(X) 1/7 1/7 1/7 1/7 1/7 1/7 1/7
What is the standard deviation of the random variable X, "the number that comes up on the die?"

User DJayC
by
7.8k points

2 Answers

1 vote

Answer:

Explanation:

the answer is 2.0

User Tenatious
by
8.9k points
2 votes
E(X) = 1/7 + 2(1/7) + 3(1/7) + 4(1/7) + 5(1/7) + 6(1/7) + 7(1/7) = 1/7 + 2/7 + 3/7 + 4/7 + 5/7 + 6/7 + 7/7 = 24/7 = 4.

Var(X) = 1/7(1 - 4)^2 + 1/7(2 - 4)^2 + 1/7(3 - 4)^2 + 1/7(4 - 4)^2 + 1/7(5 - 4)^2 + 1/7(6 - 4)^2 + 1/7(7 - 4)^2 = 9(1/7) + 4(1/7) + 1/7 + 1/7 + 4(1/7) + 9(1/7) = 9/7 + 4/7 + 2/7 + 4/7 + 9/7 = 28/7 = 4

standard deviation = sqrt(Var(X)) = sqrt(4) = 2.
User Torkel Velure
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories