Suppose Your Waiting Time for a Bus in the Morning $X _ { 1 } , \ldots X _ { 10 }$

question 7

Essay

Suppose your waiting time for a bus in the morning is uniformly distributed on [0,5], whereas waiting time in the evening is uniformly distributed on [0,10] independent of morning waiting time.
a. If you take the bus each morning and evening for a week, what is your total expected waiting time? [Hint: Define random variables $X _ { 1 } , \ldots X _ { 10 }$
and use a rule of expected value.)
b. What is the variance of your total waiting time?
c. What are the expected value and variance of the difference between morning and evening waiting times on a given day?
d. What are the expected value and variance of the difference between morning waiting time and total evening waiting time for a particular week?

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Definitions:

Nonnegotiable

Nonnegotiable describes an object or agreement that cannot be modified or transferred through negotiation, often referring to instruments like checks or securities with fixed terms.

Mortgage

A legal agreement in which property is used as collateral for a loan, with the property title transferred to the lender until the loan is repaid.

Undated

Not having a specified date, which can pertain to documents, events, or items that lack a temporal reference.

Nonnegotiable

Referring to an instrument, term, or condition that cannot be transferred or altered by agreement between the parties involved.