Consider the probability distribution below. The variance of x equals

A) 9.
B) 23.
C) 81.
D) 610.

Question

Consider the probability distribution below.   ​ The variance of x equalsA)  9.B)  23.C)  81.D)  610.

Brianna Soliz · Accepted Answer

Final Answer : C, Explanation :  To find the variance of x, we need to first find the expected value of x, denoted E(x).E(x) = Σ(xi * P(xi)) for all i from 1 to 6E(x) = (2*0.17) + (3*0.26) + (4*0.19) + (5*0.12) + (6*0.16) + (7*0.10) = 4.19Next, we need to find the squared deviations from the expected value for each possible outcome:(2-4.19)² * 0.17 = 4.36(3-4.19)² * 0.26 = 0.79(4-4.19)² * 0.19 = 0.03(5-4.19)² * 0.12 = 0.37(6-4.19)² * 0.16 = 2.02(7-4.19)² * 0.10 = 5.61The variance is the sum of these squared deviations multiplied by their probabilities:Variance = Σ[(xi - E(x))² * P(xi)] for all i from 1 to 6Variance = 4.36 + 0.79 + 0.03 + 0.37 + 2.02 + 5.61 = 13.18Thus, the variance of x is 13.18. To check our work, we can take the square root of the variance to find the standard deviation:Standard deviation = sqrt(variance) = sqrt(13.18) ≈ 3.63Note: Choice C, 81, is the square of the standard deviation, which is a common mistake. The correct answer is the variance, which is not squared.

Consider the probability distribution below. The variance of x equals

A) 9.
B) 23.
C) 81.
D) 610.

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Learning Objectives

Related questions

Consider the probability distribution below. ​ The variance of x equalsA) 9.B) 23.C) 81.D) 610.

Definitions

Learning Objectives

Learning Objectives

Related questions

Consider the probability distribution below. The variance of x equals

A) 9.
B) 23.
C) 81.
D) 610.