The Amount of Money That Maria Earns in a Week $\$ 900$

question 118

Multiple Choice

The amount of money that Maria earns in a week is a random variable,X,with a mean of $\$ 900$ and a standard deviation of $\sigma _ { \mathrm { m } }$ .The amount of money that Daniel earns in a week is a random variable,Y,with a mean of $\$ 800$ and a standard deviation of $\sigma _ { \mathrm { d } }$ .The difference, $X - Y,$ between Maria's weekly income and Daniel's weekly income is a random variable with a mean of $\$ 900 - \$ 800 = \$ 100$ If the incomes are independent of one another,which of the following shows the correct method for calculating the standard deviation of the random variable $X - Y ?$

• A)SD(X - Y)= Var(X - Y)= Var(X)+ Var(Y)= \(\sigma _ { \mathrm { m } } ^ { 2 }\) + \(\sigma _ { \mathrm { d } } ^ { 2 }\)
• B)SD(X - Y)= \(\sqrt { \operatorname { Var } ( X - Y ) }\) = \(\sqrt { \operatorname { Var } ( X ) + \operatorname { Var } ( Y ) }\)
• = \(\sqrt { \sigma _ { \mathrm { m } } ^ { 2 } + \sigma _ { \mathrm { d } } ^ { 2 } }\)
• C)SD(X - Y)= SD(X)+ SD(Y)= \(\sigma _ { \mathrm { m } }\) + \(\sigma _ { \mathrm { d } }\)
• D)SD(X - Y)= SD(X)- SD(Y)= \(\sigma _ { \mathrm { m } }\) - \(\sigma _ { \mathrm { d } }\)
• E)SD(X - Y)= \(\sqrt { \operatorname { Var } ( X - Y ) }\) = \(\sqrt { \operatorname { Var } ( X ) - \operatorname { Var } ( Y ) }\)
• = \(\sqrt { \sigma _ { \mathrm { m } } ^ { 2 } - \sigma _ { \mathrm { d } } ^ { 2 } }\)

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