Statistics

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]?

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.