1

The number of goals in a World Cup soccer match has a Poisson distribution with a mean of 3. For a soccer player in World Cup, the probability of having an age over 30 is 0.2.

a. What is the probability of having 0 goal in a World Cup soccer match? (3 pts) What is the probability of having more than 1 goal in a World Cup soccer match?

b. What is the probability that 0 out of the 11 players in a World Cup soccer team are older than 30 ?

c. The probability that a soccer team wins a World Cup match is 0.7 if none of its players are older than 30. The probability that a soccer team wins a World Cup match is 0.4 if some players are older than 30. The probability that “no players are older than 30 in a World Cup soccer team” is your result from question b. A soccer team just won the latest World Cup match. Given this information, what is the probability that NO players in the team have an age over 30?

java code:

Problem 1:

Create a class called Elevator that can be moved between floors in an N-storey building. Elevator uses a constructor to initialize the number of floors (N) in the building when the object is instantiated.

Elevator also has a default constructor that creates a five storey building.

The Elevator class has a termination condition that requires the elevator to be moved to the main (i.e., first) floor when the object is cleaned up. Write a finalize() method that satisfies this termination condition and verifies the condition by printing a message to the output, Elevator ending: elevator returned to the first floor.

In main(), test at least five (5) possible scenarios that can occur when Elevator is used in a building with many floors (e.g., create, move from one floor to another, etc.).

Tip: Termination occurs when the instance is set to null. You may wish to investigate “garbage collection” for this exercise.

An elevator has a placard stating that the maximum capacity is 1304 lb long dash—88 passengers.​ So, 88 adult male passengers can have a mean weight of up to 1304 divided by 8 equals 163 pounds.1304/8=163 pounds. If the elevator is loaded with 88 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 163 lb.​ (Assume that weights of males are normally distributed with a mean of 170  lb and a standard deviation of 32 lb​.) Does this elevator appear to be​ safe?

(please do the all questions. Thanks)

A Dice Game

a) You have been asked to create a Die class which will be used to represent dice in computer games.

The Die class should have the following fields:

• sides. The number of sides the die will have.
• value. The current value the die is displaying.

In addition, the class should have a following methods.

• A Constructor which sets the number of sides and performs an initial roll of the die.
• A roll method which is a void method that will simulate a random roll of the die.
• Accessor methods for both of the fields.

b) Write a program that uses the Die class to play a simple dice game between the computer and the user. The program should create two instances of the Die class (each a 6-sided die). One Die object is the computer’s die, and the other Die object is the user’s die.

The program should have a loop that iterates 10 times. Each time the loop iterates, it should roll both dice. The die with the highest value wins. (In case of a tie, there is no winner for that particular roll of the dice.)

As the loop iterates, the program should keep count of the number of times the computer wins, and the number of times that the user wins. After the loop performs all of its iterations, the program should display who was the grand winner, the computer or the user.

1. Queen Elizabeth has decided to auction off the crown jewels. There are two bidders: the Sultan and the Sheikh. Each will simultaneously submit a bid in a sealed envelope; the highest bidder will win, and pay what he bid. (This is a “First Price Auction”.) The Sultan is only allowed to bid an odd number: 1, 3, 5, 7, or 9. The Sheikh is only allowed to bid an even number: 2, 4, 6, 8, or 10. The Sultan places a value of 8 on the crown jewels, while the Sheikh values them at 7.Now suppose the game is a Second Price Auction instead, so the highest bidder still wins, but he pays the amount of the losing player’s bid. The players’ valuations of the jewels remain the same.

Find all Nash Equilibria of this game.

A game similar to The Wheel of Fortune is played by turning a fair wheel with 16 equal sectors labeled with numbers from 1 to 16. Each game consists of only one (1) run by turning the wheel. For each game, player wins $1200 if the needle lands on the number 1 when the wheel stops turning. Similarly, player wins $375 if the needle lands on any of the numbers 2 to 4, $170 if the needle lands on any of the numbers 5 to 8, and $60 if the needle lands on any of the numbers 9 to 14. Player wins nothing (winning $0) if the needle lands on the number 15, and gets a bankruptcy (losing $-3300) if the needle lands on the number 16. Suppose the fee is $5 to play each game. Let the random variable XX be the winning/losing amount received from this game.

A) In the table below, complete the probability distribution of XX. Leave your answer in fractions.

Table looks like this:

B) Compute the expected value of XX, E(X)E(X), from this probability distribution. Round your answer to two decimal places.
E(X)=

THIS IS A STATS PROBLEM AND I WAS UNABLE TO SOLVE IT. please solve it.

Two players, A and B alternately and independently flip a coin and the first one who flip a head on top will win. Assume player A flips first. If the coin is fair, what is the probability that A wins?If A tossed N+1 times, B tossed N times, what’s the probability that A gets more heads than B?If A and B each tosses a fair coin N times. Find the probability that they get the same number of heads.

A manufacturing process produces piston rings, with ID (inner diameter) dimension as shown above. Process variation causes the ID to be normally distributed, with a mean of 10.021 cm and a standard deviation of 0.040 cm. a. What percentage of piston rings will have ID exceeding 10.075 cm? What percentage of piston rings will have ID exceeding 10.080 cm? (4) b. What is the probability that a piston ring will have ID between 9.970 cm and 10.030 cm? (This is the customer’s specification that the supplier tries to provide .) (ie.) If the specification is “9.970cm < ID < 10.030cm”, what %’age of piston rings are “out of spec”? c. Half (50%) of all piston rings have ID below 10.021 cm. What is the dimension corresponding to the smallest 10%, and what is the dimension corresponding to the largest 10%? What is the dimension corresponding to the smallest 20%, and what is the dimension corresponding to the largest 20%

) Ben and Allison each decide to wager 1 unit against the other person on flips
of an unfair coin, with probability 0.6 of landing head, until one of them runs out of money.
When the flip lands on head, Ben wins 1 unit from Allison; and when the coin lands on tail,
Allison wins 1 from Ben. At the start of the contest, Ben has 30 units and Allison has 45
units. Find
(a) the average number of flips needed until Ben is eventually broke,
(b) the average number of flips needed until Allison is eventually broke, and
(c) the average number of flips needed until either Ben or Allison is eventually broke.

Using c# rewrite/edit the following program so that it runs the simulation 10,000 times (play the games 10,000 times) and count the number wins. Then calculate the winning probability by using the formula:

the expected winning probability = the number of wins / 10,000

using System;
class lottery
{
static void Main()
{
int n, random, choice = 1;
Random randnum = new Random();
  
while (choice == 1)
{
  
Console.Write("\nEnter a integer from 1 to 5:");
n = Convert.ToInt32(Console.ReadLine());
while (n < 1 || n > 5)
{
Console.Write("Invalid Input Enter again");
Console.Write("\nEnter a integer from 1 to 5:");
n = Convert.ToInt32(Console.ReadLine());
}
  
random = randnum.Next(1, 6);

if (n == random)
{
Console.WriteLine("You Won $5.");
}
else
{
Console.WriteLine("You lost $1");
}
Console.Write("1.To continue\n2.To exit\nEnter your choice:");
  
choice = Convert.ToInt32(Console.ReadLine());
  
}
}
}