Posted: November 25th, 2022

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You decide to move out of your college’s dorms and get an apartment, and you want to discuss the budget with your roommate. You know that your monthly grocery bill G will depend on a number of factors, such as whether you are too busy to cook, whether you invite guests for meals frequently, how many special holiday meals you will cook, etc. In particular, G will have an approximate normal distribution with a variance of 2500 and a mean:

μ=300+10M−100B+50H

Where M is the number of meals to which you invite guests, and E[M]=8. B is a measure for how busy you are and assume it is U[0,1]. H is a variable that takes on the value 1 for holiday months of November, December, and January and 0 otherwise.

Question : For a month choosen at random what is E[G]?

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a) E[300+10M-100B+50]
b) E[300+10M-100B]
c) 300+ 10E[M]-100E[B]+50E[H]
d) 312.5 + 10E[M]-100E[B]
e) E[300+10M-100B+50*3/4]
f) E[300+10M-100B+50*1/4]

Note : More than 1 correct options.

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