A plane goes missing. According to air trac control, the probability that it has gone
missing in region A is 0.2 and in region B is 0.6. From knowledge of these regions, it is
known that if a plane goes missing in region A, the probability that it will be found is 0.7,
while if a plane goes missing in region B, the probability of it being found is 0.6.
Using probability notation, answer the following questions.
(a) What is the probability that the plane did not go down in either region A or B? Justify
your answer.
(b) If the probability of the plane being found if it goes down outside regions A or B is
0.1, what is the total probability of the plane not being found at all?
(c) If the plane isn't found, what is the probability it went down in region A?
(d) If two planes go missing independently, what is the probability that they are both
found?

A plane goes missing. According to air trac control, the probability that it has gone
missing in region A is 0.2 and in region B is 0.6. From knowledge of these regions, it is
known that if a plane goes missing in region A, the probability that it will be found is 0.7,
while if a plane goes missing in region B, the probability of it being found is 0.6.
Using probability notation, answer the following questions.
(a) What is the probability that the plane did not go down in either region A or B? Justify
your answer.
(b) If the probability of the plane being found if it goes down outside regions A or B is
0.1, what is the total probability of the plane not being found at all?
(c) If the plane isn't found, what is the probability it went down in region A?
(d) If two planes go missing independently, what is the probability that they are both
found?

(1) Conditional Mean Table 1 is the probability of admission in the university. X=1 means that students are admitted; x=0 means that students are not admitted. Students are divided into two groups: male and Female.

Table 1: Admission Table

Admit . (x=1) Not Admit(x=0)

Male (0.3) . ( 0.2)

Female ( 0.4) . ( 0.1)

(a) Calculate the probability of admit, the probability of not admit, and the expectation of x.

(b)Calculate the probability of male, the probability of female, conditional probability of admit given male, conditional probability of not admit given male, conditional probability of admit given female, and conditional probability of not admit given female.

(c) Calculate the conditional expectation of x given male and the conditional expectation of x given female.

(d)Show that the expectation of x equals to the expectation of conditional expectation of x

Below you will find part of a job description for a part-time position in a campus bookstore. Read each task in the job description and identify those tasks for which training (rather than employee selection techniques) would be appropriate. In the next exercise, you will be asked to determine how to train the employees for each of the tasks you identify.

Textbook Clerk

Job Summary

The Textbook Clerk is a university work-study position. The student hired for this job is responsible for assisting the Textbook Supervisor with book inventories, shelving duties, and customer requests. Additionally, the Textbook Clerk performs general clerical and messenger duties and operates the cash register when additional assistance is needed. Work Activities

Inventory Duties - Inventories books by section and course number - Informs supervisor of number of books to be returned - Writes ISBN-13 on inventory sheet - Verifies all information as typed on each textbook requisition - Records price information

Shelving Duties - Shelves returned books - Straightens shelves - Removes previous semester's textbooks from store shelves at the end of each semester - Shelves used books in the stockroom by title - Shelves new books in the stockroom by publisher - Places shelf cards on appropriate shelf - Dusts shelves - Dusts books

Customer Relations Duties - Phones professors regarding new textbook editions - Mails book arrival notices to professors

Clerical Duties - Creates and prints shelf cards - Creates and prints book arrival notices - Types PU-6 Forms - Photocopies book orders and notices about book arrivals

Messenger Duties - Delivers materials or messages to other employees - Delivers materials to university departments 100

Cash Register Duties

- Writes name on register tab at beginning and end of shift - Watches customers entering store to make sure they do not take books and backpacks into store - Tabulates price of purchases using cash register - Counts appropriate change and gives it to customers - Pages employee on register list to assist with checkout when lines are long - Approves student's’ checks by validating university ID or by certifying driver's license - Approves out-of-town checks by verifying name, address, and phone number with driver's license - Pages supervisor to fill out void slips - Completes in-slip forms for returns - Sells laundry tickets, computer disks, and dissection coupons to students - Verifies textbook tags for price and author codes to ensure that the correct tag is still on the textbook - Pages supervisor if tag and code are incorrect

__________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ _________________________________________________________________________________

A) Fill in the blanks. (Enter an exact positive number as an integer, fraction, or decimal.)

In a normal distribution,

x = 3 and z = −1.19. This tells you that x = 3 is ________ standard deviations to the _____ (left or right) of the mean

B) Fill in the blanks. (Enter an exact positive number as an integer, fraction, or decimal.)

In a normal distribution,

x = −2 and z = 6. This tells you that x = −2 is ______standard deviations to the _____ (left or right) of the mean

C) Fill in the blanks. (Enter an exact positive number as an integer, fraction, or decimal.)

In a normal distribution,

x = 9 and z = −1.4. This tells you that x = 9 is ______standard deviations to the _____ (left or right) of the mean

D) About what percent of the x values from a normal distribution lie within two standard deviations (left and right) of the mean of that distribution? (Enter an exact number as an integer, fraction, or decimal.)

E) About what percent of x values lie between the mean and one standard deviation (one sided)? (Enter an exact number as an integer, fraction, or decimal.)

F) About what percent of x values lie between the first and third standard deviations (both sides)? (Enter an exact number as an integer, fraction, or decimal.)

G) If the area to the left of x in a normal distribution is 0.163, what is the area to the right of x? (Enter an exact number as an integer, fraction, or decimal.)

H) Use the following information to answer the next exercise.

X ~ N(54, 8)

Find the 90^th percentile. (Round your answer to two decimal places.)

I) Find the probability that x is between four and 12. (Round your answer to four decimal places.)

X ~ N(5, 3)

Each item produced by a production system goes through a quality inspection process to be classified as non-defective (ND), partially defective (PD), or totally defective (TD). Over the past several years, category percentages for a certain item produced by this system have stabilized at 85% non-defective (ND), 10% partially defective (PD), and 5% totally defective (TD). The company has purchased a new machine for producing this item. A sample of size 200 items produced by the new machine yielded 180 non-defective (ND), 16 partially defective (PD), and 4 totally defective (TD) items. We are interested to perform a goodness of fit test to determine whether the sample of 200 items produced by the new machine is consistent with the historical distribution of the number of items in each of the three categories. Let PND = probability that an item produced is non-defective (ND) PPD = probability that an item produced is partially defective (PD) PTD = probability that an item produced is totally defective (TD)

1. Refer to Exhibit 1. The null hypothesis ( H0) for the goodness of fit test is: H0: The population of items produced by the new machine follows a multinomial probability distribution with PND = 0.85, PPD = 0.10, and PTD = 0.05 . (True or False)

2. What is the expected frequency for non-defective category?

A. 170 B. 180 C. 85 D. 350

3. What is the chi square test statistic?

A. 7.888 B. 11.747 C. 43.166 D. 4.988

4. What is the critical value of the chi-square obtained from the table(or using MS Excel) for a=0.05(5% level significance)?

A. 12.592 B. 5.991 C. 7.378 D. 10.597

5. What is the p-value obtained from the chi-square table (or using MS Excel)?

A. Less than 0.05 B. More than 0.10 C. More than 0.05 but less than 0.10 D. None of the above

6. What is your conclusion?

A. The population of items produced by the new machine follows a normal probability distribution with a mean of 170 and a standard deviation of 5. B. Reject H0, the population of items produced by the new machine does NOT follow a multinomial probability distribution with PND = 0.85, PPD = 0.10, and PTD = 0.05 . C. Do NOT reject H0; the population of items produced by the new machine follows a multinomial probability distribution with PND = 0.85, PPD = 0.10, and PTD = 0.05 . D. The results of the test are inconclusive.

(1) Read in the data and create an R data frame named tennis.dfr 
that has the following names for its columns:  first.name, last.name,
major.match.wins, major.match.losses, overall.match.wins, 
overall.match.losses, major.titles, overall.titles.  (Note that the 
data file has several explanatory lines before the real data begin 
that should be skipped when reading in the data lines.)
NOTE:  For the file name, you must use the following web address (URL): 
"http://people.stat.sc.edu/hitchcock/tennisplayers2018.txt".  
Please do not have your code read in the file from your own personal directory.

(2) Create and add two more columns called major.winning.pct and 
overall.winning.pct (showing winning percentage in the "major" and 
"overall" categories, respectively) to this data frame.
  
Note that "winning percentage" is defined 
as (match wins)/(match wins + match losses).

(3) Sort the data frame by major titles, from most to least.  
Have your program print the sorted data frame.

(4) Perform a nested sort, sorting the data frame first by major
titles (from most to least), and then by major winning percentage 
(from most to least) within major-title levels.
Have your program print this sorted data frame.

(5) Have R extract the subset of the data frame consisting of players
with at least 6 major titles.  Call this new data frame: greatest.dfr
Have your program print this new data frame.

(6)  In the most efficient way possible, have R calculate the sample means 
for each of the numeric variables in the tennis.dfr data set.
(Hint: Extract the appropriate subset of the data frame first.)

(7) Use the write.table() function to write the data set tennis.dfr to an
external file simply called "tennisdata.txt".  Make sure the external file includes the column names.
Also, make sure the players' names are NOT surrounded by quotes in the 
external file.

import random

play = True
while play:       #create a new game if play is True
   turn = 0
   remaining_coins = random.randint(20, 30)   #randomly generate coins between 20 to 30
   print("Take turns removing 1, 2, or 3 coins,")
   print("You win if you take the last coin.")

   while remaining_coins > 0:       #loop until remaining_coins exist
       print("\nThere are", remaining_coins, "coins remaining. ")
       if turn % 2 == 0:                                                           #player 1 move
           taken_coins = int(input("Player 1: How many coins do you take? "))  
       else:                                                                       #player 1 move
           taken_coins = int(input("Player 2: How many coins do you take? "))

       while taken_coins < 1 or taken_coins > 3 or taken_coins > remaining_coins:   #Invalid move, ask again
           print("That's not a legal move. Try again. ")
           print('\nThere are', remaining_coins, 'coins remaining. ')
           if turn%2 == 0:
               taken_coins = int(input ("Player 1: How many coins do you take? "))
           else:
               taken_coins = int(input("Player 2: How many coins do you take?" ))

       if remaining_coins - taken_coins == 0:   #if all coings got over, annnounce the winner
           print("No more coins left!")
           if (turn % 2) == 0:
               print('Player 1 wins!')
               print('Player 2 loses!')
           else:
               print("Player 2 wins!")
               print('Player 1 loses!')
      
       remaining_coins = remaining_coins - taken_coins   #update remaining_coins and turn
       turn += 1
   inp = input('\nDo you want to play again(Y/N)? : ')   #ask if users wants to play again, Y:Yes, N:No
   if inp == 'Y' or inp == 'y':
       play = True
   else:
       play = False

How can I get the program to have the computer play with the user? The code above allows you to be player 1 and player 2, but I want the code to have the computer be assigned to one player, so it can play with the other player

fix this code in python and show me the output. do not change the code

import random

#variables and constants

MAX_ROLLS = 5
MAX_DICE_VAL = 6

#declare a list of roll types

ROLLS_TYPES = [ "Junk" , "Pair" , "3 of a kind" , "5 of a kind" ]

#set this to the value MAX_ROLLS

pdice = [0,0,0,0,0]
cdice = [0,0,0,0,0]

#set this to the value MAX_DICE_VAL

pdice = [0,0,0,0,0,0]
cdice = [0,0,0,0,0,0]

#INPUT - get the dice rolls

i = 0
while i < MAX_ROLLS:
pdice[i] = random.randint(1, MAX_DICE_VAL)
cdice[i] = random.randint(1, MAX_DICE_VAL,)
i += 1
#end while

#print the player's and computer dice rolls

i = 0
print ( "Player rolled: ", end=" " )
while i < MAX_ROLLS:
print( pdice[i], end = " " )
i += 1
#end while
print ("\n")

i = 0
print ("Computer rolled: ", end=" " )
while i < MAX_ROLLS:
print( cdice[i], end = " " )
i += 1
#end while
  
#load the tally list so we can determine pair, 3 of a kind, etc
i = 0
while i < MAX_ROLLS:
ptally [ pdice[i] - 1 ] += 1
ctally [ cdice[i] - 1 ] += 1
i += 1
#end while

# find out pair, 3 of kind, etc
pmax = ptally[0] # init to first element in tally array
cmax = ctally[0]

i = 1
while i < MAX_DICE_VAL:
if pmax < ptally[i]:
pmax = ptally[i]
#end if

if cmax < ctally[i]:
cmax = ctally[i]
i += 1
#end while
  

#output - display what was rolled and who won
print("\n")
print(" player rolled: " + ROLL_TYPES[ pmax - 1], end="\n" )
print(" computer rolled: " + ROLL_TYPES[ cmax - 1] )

# determine the winner
if pmax > cmax:
print( "player wins!", end="\n" )
elif cmax > pmax:
print (" computer wins!", end="\n" )
else:
print("Tie!", end="\n" )

Calculate the mean and variance of the following cash flows.

A 20% probability of making $100, a 30% probability of making $200, a 10% probability of making $500, and a 40% probability of losing $50