All ships travel at the same speed through a wide canal. Each ship takes days to traverse the length of the canal. Eastbound ships (i. e., ships traveling east) arrive as a Poisson process with an arrival rate of ships per day. Westbound ships (i. e., ships traveling west) arrive as an independent Poisson process with an arrival rate of ships per day. A pointer at some location in the canal is always pointing in the direction of travel of the most recent ship to pass it. In each part below, your answers will be algebraic expressions in terms of and/or . Enter 'LE' for and 'LW' for , and use 'exp()' for exponentials. Do not use 'fac()' or '!' for factorials; instead, calculate out the numerical value of any factorials. Follow standard notation.

For parts (1) and (2), suppose that the pointer is currently pointing west.

1) What is the probability that the next ship to pass will be westbound?
2) Determine the PDF, , of the remaining time, , until the pointer changes direction.
For the remaining parts of this problem, we make no assumptions about the current direction of the pointer.

3) What is the probability that an eastbound ship does not pass by any westbound ships during its eastward journey through the canal?
4) Starting at an arbitrary time, we monitor the cross-section of the canal at some fixed location along its length. Let be the amount of time that will have elapsed (since we began monitoring) by the time we observe our seventh eastbound ship. Determine the PDF of .
5) What is the probability that the next ship to arrive causes a change in the direction of the pointer?

6) If we begin monitoring a fixed cross-section of the canal at an arbitrary time, determine the probability mass function for , the total number of ships we observe up to and including the seventh eastbound ship we see. The answer will be of the form , for suitable algebraic expressions in place of and .

What is the relationship between atmospheric pressure and the density of gas particles in an area of increasing pressure? (2 points) as air pressure in an area increases, the density of the gas particles in that area decreases. as air pressure in an area increases, the density of the gas particles in that area increases. as air pressure in an area increases, the density of the gas particles in that area remains constant. as air pressure in an area increases, the density of the gas particles in that area increases and decreases in an alternating pattern. 3. which of the following correctly describes a way in which earth's atmosphere interacts with the geosphere? (2 points) it contains gases that living organisms breathe. it contains gases that trap incoming solar radiation. it provides a medium for cycles that provide nutrients to living organisms. it provides a medium for water to move between earth's surface and the air. 4. which of the following is considered a drawback to using wind energy as a source of power? (2 points) wind energy is nonrenewable. wind energy produces large amounts of air pollution. wind turbines can kill birds that fly through the rotors. wind turbines are built too close to major population centers. 5. a meteorologist predicts that the weather in a region will soon change from clear skies to probable thunderstorms. prior to making this prediction, what did the meteorologist most likely observe on a barometer? (2 points) the barometer fell slightly. the barometer fell substantially. the barometer rose slightly. the barometer rose substantially. 6. which of the following do meteorologists not typically use weather balloons to record? (2 points) atmospheric pressure cloud types humidity temperature 7. during which step in the can crush lab did water vapor force air from the can? (2 points) the can was filled nearly to the top with water. the can was placed on the hot stove top burner for several minutes. the can was removed from the hot stove top burner. the can was placed upside-down in the water-filled pan.

The space between two 15-in.-long concentric cylinders is filled with glycerin (viscosity = 8.5 × 10-3 lb·s/ft2). the inner cylinder has a radius of 1 in. and the gap width between cylinders is 0.1 in. determine (a) the torque and (b) the power required to rotate the inner cylinder at 180 rev/min. the outer cylinder is fixed. assume the velocity distribution in the gap to be linear.

Which are true about beta reactions? there will be more than one answer. a. it has no change b. it doesn't change the mass of the number c. it has a mass of 0.0005 atoms d. it causes transmutation.