(A)
The expected value of each option is to be calculated.
(A)
Explanation of Solution
Expected value is calculated as
Consider an option 1,
=
Consider an option 2,
Therefore, in both the options, expected value is 450.
(B)
The variance and standard deviation of each option is to be calculated.
(B)
Explanation of Solution
Variance is calculated as
σ = [ q1(x1 - (E(x))2 + q2(x2 - (E(x))2 + ................+ qn(xn - (E(x))2 ]
Standard deviation is the square root of variance.
SD =
Consider an option 1,
σ =
=
=
=
=
Consider an option 2,
σ =
=
=
=
=
Variance in option 1 is 157500 and in option 2 is 279270.
Standard deviation is the square root of variance.
SD = v σ
Consider an option 1,
Consider an option 2,
Variance of option 1 is 157500 and variance of option 2 is 279270.
Standard deviation of option 1 is 396.86 and standard deviation of option 2 is 528.46.
(C)
The option that is riskier to be ascertained.
(C)
Explanation of Solution
Basically, the option with high variability is more risky option.
Higher variability means high variance or standard deviation.In this question, Option 2 has more variance and standard deviation. Thus, it is riskier.
The riskier option is Option 2.
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