6. 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. (i.e. Find E[X]) b) 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 c) Find E[M] and E[W]. d) Find V[M] and V[W]. e) 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.

6. 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. (i.e. Find E[X]) b) 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 c) Find E[M] and E[W]. d) Find V[M] and V[W]. e) 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

If 2 of 20 tires are defective and 8 of them are randomly chosen for inspection.what is the probability that both of the defective tires will be chosen.. (Round to three decimals)
Assume That when adults with smart phones are randomly selected, 52% use them in meetings or classes. If 25 adult smart phone users are randomly selected, find the probability that exactly 16 of them use their smart phones in meetings or classes. The probability is?( round to 4 decimal spaces)
Suppose that a box contains 8 cameras and that 4 of them are defective. A sample of 2 cameras is selected at random. Define the random variable Xas the number of defective cameras in the sample. Write the probability distribution for X.Write your answer in fraction form or round to 3 decimal places.
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.)
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 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 factory produces a particular electrical component. On average, the probability that a component will be faulty is 0.16, independently of each other. The company sells the electrical component in a box of 7. Calculate the probability of having at least 1 faulty components. (2 d.p.)
Let be a lot of 20 defective items and 80 non-defective items, of which 2 are chosen without replacement. Find the probability that the second item chosen is defective.
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 factory produces a particular electrical component. On average, the probability that a component will be faulty is 0.16, independently of each other. The company sells the electrical component in a box of 7. Calculate the probability of having at least 1 faulty components. (2 d.p.)
A jar contains 12 coins: 6 pennies, 2 nickels and 4 dimes. A child selects 2 coins at random without replacement from the jar. Let X be the sum of the value of the 2 coins. Determine the probability distribution of X. Please enter the values for x in increasing order. Round your answers to three decimal places, if necessary. Hint: If you are picking two different coins, remember that you can pick one first, then the other or the other way around, and you will still end up with the same two coins. X P(X = x) 2 0.015 If you were to randomly draw two coins from this jar, how many cents do you expect to have on average? (Averages of discrete things CAN be decimals!)
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)