You are playing rock, paper, scissors (RPS) with a friend. Because you are good at predicting your friend’s strategy, there is a 60% chance each time that you play her, that you win. You play 7 games of rock, paper scissors with your friend and would like to know how many of them you win. Use this information to answer the following questions.

1. What is the random variable in this example?
a. X = number of times your friend wins at RPS
b. X = wins
c.X = times you win
d. X = number of times you win at RPS

2. What kind of random variable is X?
a. Discrete
b. Continuous - unbounded
c. Continuous - bounded

3. For this problem, what would constitute a success and what is the probability that a success occurs?
a. Your friend winds a game of RPS, 60%
b. Your friend winds a game of RPS, 40%
c. You win a game of RPS, 40%
d. You win a game of RPS, 60%

4. What is the distribution of the random variable?
a. X ~ negbin(7, 0.6)
b. X ~ binomial
c. X ~ bin(7, 0.6)
d. X ~ bin(3, 0.6)

5. What is the probability that you win exactly three of the seven games played? (To four decimal places)

6. What is the probability that you win five or fewer games? (To four decimal places)

Consider the Monty Hall problem.Verify the results using by writing a computer program that estimates the probabilities of winning for different strategies by simulating it.

1. First, write a code that randomly sets the prize behind one of three doors and you also randomly select one of the doors. You win if the the door you selected has the prize (Here, we are simulating ’stick to the initial door’ strategy). Repeat this experiment 100 times and compute the average number of wins.

2. Next, try simulating the switching strategy. Find the door the host will open and change your initial door with the door not opened by the host. Also repeat this experiment 100 times and compute the average number of wins. If you did everything right, the first code should yield the probability of winning as ≈ 1/3 and the second code should yield ≈ 2/3. You can use any programming language you want (MATLAB, Python etc.)

1. Circular motion
   1. If 1 metric ton elevator is accelerating upwards at 7.0 m/s², Calculate the force of tension in the cable.
   2. If the elevator is accelerating downwards at 7.0 m/s² calculate the force of tension in the cable.
   3. Describe the acceleration that is most likely to break the elevator cable.
   4. Now imagine the elevator is in Willy Wonka’s chocolate factor and it can move in any direction. If the elevator is moving at a speed of 3.5 m/s around a curve with a radius of 18 ft, what will the centripetal acceleration of the elevator be?
   5. What will the centripetal force of the elevator be?
   6. If the radius of the curve and the speed of the elevator both double, what will happen to the centripetal force?

1. 1)A casino wants to introduce a new game. In this game a player rolls two 4-sided dice and their winnings are determined by the following rules:
   1. Otherwise, the player wins nothing.
   2. If 3 ≤ sum ≤ 5 the player wins $25.
   3. If sum ≥ 6 the player wins $100.

1. a)Determine the probability distribution for this gamble.

b)How much should the casino charge for this game if they want to make a profit in the long run? Show the calculations that support your decision

c)What is the standard error, σ_X, for this gamble

1. Complete the probability distribution for X below.

2. Compute: (i) P (X ≤ 3) and (ii) P (X < 3)

3. Compute: P (X > 1)

4. Compute: P (X is odd)

5. Compute the expected value and variance of X.

1. Assume the average number of years that nurses have worked at their job is normally distributed with a mean of 21 years and a population standard deviation of 12 years. Suppose we take a sample of 15 nurses.
   1. What is the probability that a randomly selected nurse will have worked for more than 30 years?
   2. What is the probability that a randomly selected nurse will have worked for under 5 years?
   3. What is the probability that a randomly selected nurse has worked between 10 and 25 years?
   4. What is the probability that the average number of years nurses have worked in the sample is above 25?
   5. What number of years worked defines the lowest 34.09% of the distribution for an individual nurse?
   6. What number of years worked defines the highest 7.93% of the distribution for an individual nurse?

1. Consider a sealed-bid auction in which the winning bidder pays the average of the two highest bids. As in the auction models considered in class, assume that players have valuations v1 > v2 > ... > vn, that ties are won by the tied player with the highest valuation, and that each player’s valuation is common knowledge.

   1. Is there any Nash equilibrium in which the two highest bids are different? If there is, give an example. If there is not, prove that no such equilibrium exists.

   2. Is there any Nash equilibrium in which a player other than the one with the highest valuation wins? If there is, give an example. If there is not, prove that no such equilibrium exists.

   3. Will bidding more than one’s own valuation be weakly dominated in this auction? Will bidding one’s own valuation exactly be weakly dominated? Will bidding less than one’s own valuation be weakly dominated?

   4. What is the highest possible winning bid in any Nash equilibrium of this game? What is the lowest possible winning bid in Nash equilibrium.

On PC1, start a continuous ping to 192.168.1.1 and 2001:db8:acad:1000::1

I know about the -t switch to make a continuous ping, but how do I get both pings going at the same time? This is for a lab and one of the steps is the one above, but I wasn't aware you could have 2 continuous pings going on on the same PC without stopping one of them. What's the command I should use? I know I should use Ping 192.168.1.1 -t to start the first ping, and ctrl c stops it, but how do I get both going at once? Thanks

Provide a diagram for each situation. A 45kg woman is riding on an elevator. What are her net force, force of gravity, and normal force for her when:

1) The elevator is stationary on the 20th floor of a building

2) The elevator has a downward acceleration with a magnitude of 1.5 meters per second squared.

3) The elevator has a constant downward velocity of 3 meters per second.

4) The elevator accelerates upward with a magnitude of 1.5 meters per second squared to stop at the 5th floor

5) The elevator cable suddenly breaks and the elevator undergoes free fall/

The following table shows the number of wins eight teams had during a football season. Also shown are the average points each team scored per game during the season. Construct a​ 90% prediction interval to estimate the number of wins for teams that scored an average of 27 points a game.