A discrete random variable named X has the following pmf (probability mass function):

17a) Find P(X>6)

17b) What is the probability two independent observations of X will both equal 1?

17c) Find the population mean also known as E(X)= the expected value of

17d) Find the population variance of X with both the “regular” formula and “convenient”

formula

Make a table and show your work. You should get the same answer with both

formulas. Finally, find the standard deviation.

4. A) The probability that a student from a certain university has a cell phone is 0.2. So, the probability that the tenth student randomly interviewed at this university is the fifth with Cell phones is:

B) On a certain day, the second stage of the environmental contingency plan was implemented in the Mexico City. If there are 50 companies in the area that corresponds to a supervisor, of which 15 did not follow contingency guidelines, then the probability that 3 companies out of the 10 that are verified will not follow the guidelines is:

C)If the planes arriving at an airport follow a Poisson process with an average rate of 8 planes per hour. The probability of exactly 10 aircraft arriving in the next 2 hours is as close to:

A battery is constructed from these two half reactions:

            i.   VO²⁺   +   2 H⁺ + e-   → V³⁺   + H₂O        E^o = 0.337 V vs SHE

            ii.   TiF₆^{2 ̶}   +   4 e-   →   Ti(s) + 6 F ^̶                           E^o = ̶ 1.191 V

(a) (0.2 pt) Which half reaction is in the anode compartment?   Circle one:     vanadium rxn      titanium rxn

(b) Which half reaction is in the cathode compartment? Circle one:    vanadium rxn      titanium rxn

(c) Write the balanced chemical equation for the overall battery reaction.

(d) Show the shorthand notation for representing this particular battery:

(e) Calculate the E^o of the battery.

1.      If your firm calculates its Economic Capital due to Market Risk, Credit Risk, Operational Risk for the next 1 year as follows . . .    (10 points)

                  Market Risk           $323,000

                  Credit Risk             $515,000

                  Operational Risk    $ 83,270

         . . . what will be the firm's total Economic Capital . . .

         a.      If the correlations among the three types of capital are believed to be :

                  Market-Credit        0.4

                  Market-Operation 0.1

                  Credit-Operation   0.2

b.      If the correlations are all equal to 1.0:

d.      If you don't know the correlations, which measure is probably too high? which is                               probably too low? what might be a reasonable level to use?

A computer is shared by 2 users who send tasks to a computer remotely and work independently. At any minute, any connected user may disconnect with probability 0.5, and any disconnected user may connect with a new task with probability 0.2. Let X(t) be the number of concurrent users at time t (in minutes). This is a Markov chain with 3 states: 0, 1, and 2. The probability transition matrix can be calculated and it is Generate 10000 transitions of the Markov chain. What percent of times do you find your generated Markov chain in each of its 3 states? Write using R code.

Q4.(15) One random sample of the hours of one type of user watch TV per day was recorded: 2.9, 3.5, 3, 3.2, 3.3, 3.5, 3.3, 3, 3.5.

1.(5) Apply the backward empirical rule to check normality of the data, and conclude if any evidence of non-normality.

2.(5) Assume that the underlying population is normal. Find a two-sided 99% confidence interval for the the true population average hours

3.(5) Assume that population variance σ2=0.09σ2=0.09 and the bound on the error of estimation of 99% confident interval to be 0.2. Find the minimum sample size nn.

A capacitor consists of two concentric spherical shells. The outer radius of the inner shell is a = 0.1 m and the inner radius of the outer shell is b = 0.2 m. a. What is the capacitance, C, of this capacitor? b. Suppose the maximum possible electric field at the outer surface of the inner shell before the air starts to ionize E max(r=a) = 3.0*10^6 V/m . What is the maximum possible charge on the inner capacitor? c. What is the maximum amount of energy stored in this capacitor? d. When E (r=a) = 3.0*10^6 V/m, what is the potential difference between the shells?

Pete Corp. issued $30 million of 7%, 15-year convertible bonds at 102 on January 1, 2021. The bonds pay interest semiannually each June 30 and December 31. Each $1,000 bond is convertible into 50 shares of Pete's no par common stock. Pete recently issued similar, but non-convertible, bonds at 98.  

61 % of the bonds were converted when the common stock had a price of $23/share and the remaining premium was $0.2 million ($200,000).

For what amount would Pete credit Common Stock when 61% of the bonds are converted?

Enter in dollars (e.g. enter $10 million as 10,000,000).

Two long, straight wires are perpendicular to the plane of the paper and at a distance 0.2 m from each other, as shown in the figure. The wires carry currents of I1 = 2.6 A and I2 = 5 A in the direction indicated (out of the page). Find the magnitude and direction of the magnetic field (in µT) at a point A midway between the wires. You need to indicate the direction with a positive or a negative value for the magnetic field. Keep in mind that a vector is positive if directed to the right and negative if directed to the left on the x axis and it is positive if directed up and negative if directed down on the y axis. Your answer should be a number with two decimal places, do not include the unit.

The following are the load and gage lengths from a stainless steel. The diameter of the bar is 0.506 inch. Plot engineering stress versus engineering strain for the data shown. Find the 0.2% offset yield strength for this steel.