1. Players A and B each roll a fair 6-sided die. The player with the higher score wins £1 from the other player. If both players have equal scores, the game is a draw and no one wins anything.

i. Let X denote the winnings of player A from one round of this game. State the probability mass function of X. Calculate the expectation E(X) and variance Var(X).

ii. What is the conditional probability that player A rolls a 2 , given that player B wins.

iii. Suppose the game is repeated 10 times. Compute the probability that at least two of the rounds result in draws.

Three persons, A, B, and C, take turns in throwing a die. They throw in the order A, B, C, A, B, C, A, B, etc., until someone wins. A wins by throwing a "one". B wins by throwing a "one" or a "two". C wins by throwing a "one", a "two", or a "three". Find the probability that each of the players is the winner.

Suppose to get 3/13, 5/13, 5/13

System Administration Linux/Unix

This lab is for you to research and implement old school DNS for your virtualized environment

Currently, if you tried to ping your server01 by IP address (192.168.10.11), you would receive a response. If you tried to ping using its hostname "server01", it would result in "ping: hostname: Temporary failure in name resolution"

1) Research how and where to implement

2) Create the following entries:

192.168.10.1 router

192.168.10.11 SRV1

192.168.10.12 SRV2

192.168.10.13 client

3) Ensure these hostnames work from each VM and verify with screenshot(s).

A screenshot from each VM (except the router) should show the result of

ping router

ping srv1

ping srv2

ping client

Connor is a statistics student interested in the number of games won by each team per season during the past 12 years for a certain professional baseball league. He records the total number of wins x for each team each season and the probability of each value P(x), as shown in the table provided. Use Excel to find the mean and the standard deviation of the probability distribution. Round the mean and standard deviation to three decimal places. Number of wins, x P(x) 54 0.003 55 0.009 56 0.015 57 0.012 58 0.006 59 0.018 60 0.024 61 0.036 62 0.027 63 0.045 64 0.036 65 0.045 66 0.039 67 0.054 68 0.051 69 0.060 70 0.054 71 0.071 72 0.059 73 0.045 74 0.042 75 0.030 76 0.033 77 0.036 78 0.027 79 0.024 80 0.021 81 0.018 82 0.012 83 0.015 84 0.015 85 0.009 86 0.006 87 0.003

The accompanying data are the number of wins and the earned run averages​ (mean number of earned runs allowed per nine innings​ pitched) for eight baseball pitchers in a recent season. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given​ x-values, if meaningful. If the​ x-value is not meaningful to predict the value of​ y, explain why not.

​(a) x=5 wins

​(b) x=10 wins

​(c) x=21 wins

​(d) x=15 wins

Wins, x= 20 18 17 16 14 12 11 9

Earned run average, y= 2.74 3.31 2.65 3.64 3.94 4.34 3.88 5.16

1. Find the regression equation.

2. Graph below

The accompanying data are the number of wins and the earned run averages​ (mean number of earned runs allowed per nine innings​pitched) for eight baseball pitchers in a recent season. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given​ x-values, if meaningful. If the​ x-value is not meaningful to predict the value of​ y, explain why not. ​(a) x=5 wins (b) x=10wins (c) x=21 wins (d) x=15 wins

The equation of the regression line is y = (__) x + (__).

20, 2.72
18 3.26
17 2.72
16 3.75
14 3.83
12 4.41
11 3.73
9 5.07

The accompanying data are the number of wins and the earned run averages​ (mean number of earned runs allowed per nine innings​ pitched) for eight baseball pitchers in a recent season. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given​ x-values, if meaningful. If the​ x-value is not meaningful to predict the value of​ y, explain why not.

​(a) x=5 wins ​(b) x=10 wins ​(c) x=21 wins ​(d) x=15 wins. The equation of the regression line is y with equals ____xplus ______. ​(Round to two decimal places as​ needed.)

The accompanying data are the number of wins and the earned run averages (mean number of earned runs allowed per nine innings pitched) for eight baseball pitchers in a recent season. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values. If meaningful. If the x-value is not meaningful to predict the value of y, explain why not. (a) x=5 wins (b) x=10 wins (c) x=21 wins (d) x=15 wins

The equation of the regression line is y= ? x+? (Round to two decimal places as needed.)

a. Predict the ERA for 5 wins, if it is meaningful.Select the correct choice below and ,if necessary, fill in the answer box within your choice.

A. ^y= ? (Round to two decimal places as needed.)

B. it is not meaningful to predict this value of y because x=5 is well outside the range of the original data.

C. It is not meaningful to predict this value of y because x=5 is not an x-value in the original data.

(b) Predict the ERA for 10 wins, if it is meaningful.Select the correct choice below and, if necessary, fill in the answer box within your choice.

A. y^= ? (Round to two decimal places as needed.)

B. it is not meaningful to predict this value of y because x=10 is not an x-value in the original data.

C. it is not meaningful to predict this value of y because x=10 is inside the range of the orginal data.

(c) Predict the ERA for 21 wins, if it is meaningful. Select the correct choice below and, if necessary, fill in the answer box within your

choice.

A. y^= ? (Round to two decimal places as needed.)

B. It is not meaningful to predict this value of y because x=21 is not x-value in the original data.

C. it is not meaningful to predict this value of y because x=21 is well outside the range of the original data.

(d) Predict the ERA for 15 wins, if it meaningful. Select the correct choice below and,if necessary,fill in the box within your choice.

A. y^= ? (Round to two decimal places as needed.)

B. It is not meaningful to predict this value of y because x=15 is inside the range of the original data.

C. It is not meaningful to predict this value of y because x=15 is not an x-value in the original data.

Wins, x Earned run average, y

20, 2.82

18, 3.24

17, 2.56

16, 3.65

14, 3.79

12, 4.34

11, 3.78

9, 5.07

Three persons, A, B, and C, take turns in throwing a die. They throw in the order A, B, C, A, B, C, A, B, etc., until someone wins. A wins by throwing a "one". B wins by throwing a "one" or a "two". C wins by throwing a "one", a "two", or a "three". Find the probability that each of the players is the winner.

The answers are 3/13, 5/13, 5/13

Please show your work

Question 1610 pts

In 14 trials, what is the probability of 5 successes, 1 failure, 3 successes, 1 failure, and 4 successes, in that exact order?

Group of answer choices

0.00312

0.00357

0.00401

0.00288

0.00165

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_______________________________________________________________________________________

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In Roulette there are 38 slots: 18 red, 18 black, and 2 green. Suppose you play and bet on red 1000 times.

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Question 1710 pts

How many times would you expect to win in 1000 plays?

Group of answer choices

500

485

474

499

526

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Question 1810 pts

How far will your actual number of wins be from your expected number of wins?

Group of answer choices

5.28

15.79

10.41

16.33

13.27

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Question 1910 pts

What is the probability of winning fewer than 447 times?

Group of answer choices

0.0436

0.9772

0.0228

0.8869

0.9429

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Question 2010 pts

What is the probability of winning between 447 and 468 times?

Group of answer choices

0.3402

0.2543

0.2325

0.3084

0.2751