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:

Blood Pressure

indicates the force exerted by circulating blood on the walls of blood vessels, a crucial indicator of cardiovascular health.

Anterior Hypothalamus

A region in the brain that plays a critical role in regulating temperature, reproductive behavior, and sleep.

Sexual Behavior

Actions that individuals engage in that are related to their sexuality or sexual activities.

Medial Preoptic Area

A region of the hypothalamus involved in regulating behaviors such as mating, thermoregulation, and hormone secretion.