1. There are two boxes. In each box there are 4 cards with a different number printed on it. The four cards have been numbered as 1,2,3,4 in each box. Two cards are drawn random from each box. The random variable X represents the difference between the number on the card from box 1 minus the number on the card from box 2. a) Find the mean of this probability distribution. (ie. Find E[X]). Find the variance and standard deviation of this probability distribution. (i.e. Find V[X] and SD[X]) The random variables M and W are defined as follows: M=X+5 and W = (1/2)X+5 Find E[M] and E[W]. Find V[M] and V[W]. Mary and William play a game using the cards in the above boxes. Randomly two cards are drawn, and Mary records his score using the random variable M and William uses the random variable W. They repeat this for a large number of times and compare their scores. Comment on any likely differences or similarities of their scores

1. There are two boxes. In each box there are 4 cards with a different number printed on it. The four cards have been numbered as 1,2,3,4 in each box. Two cards are drawn random from each box. The random variable X represents the difference between the number on the card from box 1 minus the number on the card from box 2. a) Find the mean of this probability distribution. (ie. Find E[X]). Find the variance and standard deviation of this probability distribution. (i.e. Find V[X] and SD[X]) The random variables M and W are defined as follows: M=X+5 and W = (1/2)X+5 Find E[M] and E[W]. Find V[M] and V[W]. Mary and William play a game using the cards in the above boxes. Randomly two cards are drawn, and Mary records his score using the random variable M and William uses the random variable W. They repeat this for a large number of times and compare their scores. Comment on any likely differences or similarities of their scores

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Suppose that 2 defective microwaves have been included in a shipment of 6 microwaves. The buyers want to test the 6 microwaves one at a time. Let Y denote the number of defective microwaves is found after 3 random selected ones have been tested. a. Calculate the probability that the buyers can find at least 1 defective microwave after 3 have been tested? b. Find the probability that buyers cannot find any defective microwave after 3 random ones have been tested?
Assume that when adults with smartphones are randomly selected, 45% use them in meetings or classes. If 9 adult smartphone users are randomly selected, find the probability that at least 2 of them use their smartphones in meetings or classes. The probability is. (Round to four decimal places as needed.)
The solution already uploaded was not that clear.... Question: A small commuter airline flies planes that can seat up to 8 passengers. The airline has determined that the probability that a ticketed passenger will not show up for a flight is 0.2. For each flight the airline sells tickets to the first 10 people placing orders. The probability distribution for the number of tickets sold per flight is shown in the accompanying table. For what propor- tion of the airline’s flights does the number of ticketed passengers showing up exceed the number of avail- able seats? (Assume independence between the num- ber of tickets sold and the probability that a ticketed passenger will show up.) Number of tickets: 6, 7, 8, 9, 10 Probability: 0.25, 0.35, 0.25, 0.10, 0.05
In a pastry shop in a small town, the probability that a customer buys apple tarts is0.45, the probability they buy an apple pie is 0.69 and the probability that they buy bothan apple tart and an apple pie is 0.27. A customer is chosen at random.i. Find the probability that they buy an apple tart or an apple pie. ii. Given that a customer buys an apple pie, what is the probability that they alsobuy an apple tart? b) The weight of a green forest frog has a normal distribution with mean 150.3 g and astandard deviation of 5g. Find the probability that a randomly selected frog weighsi. Less than 153g ii. Between 150 g and 158 g c) The random variable X is normally distributed such that X~N(?, 12). It is known that?(? > 32) = 0.0618. find the value of ?.
A jar contains 16 coins: 8 pennies, 5 nickels and 3 dimes. A child selects 2 coins at random without replacement from the jar. Let XX be the sum of the value of the 2 coins. Determine the probability distribution of XX. Please enter the values for xx in increasing order. Please enter the values for p(x)p(x) as a number rounded to four decimal places.
There are two boxes. Box A contains 6 red balls, and 4 blue balls andBox B contains 4 red balls and 8 blue balls. A die is rolled, if the number is lessthan 3, a ball is selected from box A. If the result is 3 or more, a ball is selectedfrom Box B. Calculate:a. The probability that the ball will be red and selected from Box B.b. The probability that the ball will be blue.
A physics class has 50 students. Of these, 11 students are physics majors and 16 students are female. Of the physics majors, three are female. Find the probability that a randomly selected student is female or a physics major. The probability that a randomly selected student is female or a physics major is (Round to three decimal places as needed.) ******************
A study conducted at a certain college shows that 54% of the school's graduates move to a different state after graduating. Find the probability that among 5 randomly selected graduates, at least one moves to a different state after graduating. Round to three decimal places as needed. А. 0.200 В. 0.540 C. 0.979 D. 0.954
The probability that a homeowner owns a lawnmower is 0.6. The probability that a homeowner owns a weed wacker is 0.7. The probability that a homeowner owns both a lawnmower and a weed wacker is 0.4. If a homeowner is selected at random, what is the probability that he or she ownseither a lawnmower or a weed wacker?
Nissa is randomly pulling the medical records of a hospital's patients and collecting the records of those who have multiple stays at this hospital. Assume that 27% of all patients who have ever stayed at this hospital have multiple stays. What is the probability that the first multiple stays patient record that Nissa comes across is the fourth one she pulls? Use a TI-83, TI-83 Plus, or TI-84 calculator to find the probability. • Round your answer to three decimal places.
A math class consists of 25 students, 14 female and 11 male. Three students are selected at random to participate in a probability experiment. Compute the probability that three females are selected. Probability of first student being a female = (as a fraction) Probability of second student being a female = (as a fraction) Probability of third student being a female = (as a fraction) Probability that three females are selected = (as a decimal rounded to the nearest thousandth)
Assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes. If 10 adult smartphone users are randomly selected, find the probability that at least 8 of them use their smartphones in meetings or classes. The probability is. (Round to four decimal places as needed.)