Let \( X \) be the number of packages being mailed by a randomly selected customer at a shipping facility. Suppose the distribution of \( X \) is as follows:\[\begin{array}{c|cccc}x & 1 & 2 & 3 & 4 \\\hlinep(x) & 0.4 & 0.3 & 0.2 & 0.1 \\\end{array}\](a) Consider a random sample of size \( n = 2 \) (two customers), and let \( \bar{X} \) be the sample mean number of packages shipped. Obtain the probability distribution of \( \bar{X} \).(b) Refer to part (a) and calculate \( \Pr(\bar{X} \leq 2.5) \).(c) Again consider a random sample of size \( n = 2 \), but now focus on the statistic \( R \), the sample range (difference between the largest and smallest values in the sample). Obtain the distribution of \( R \).(d) If a random sample of size \( n = 4 \) is selected, what is \( \Pr(\bar{X} \leq 1.5) \)? [Hint: you should not have to list all possible outcomes, only those for which \( \bar{x} \leq 1.5 \).]

Given Let x be the number of packages being mailed by a randomly selected customer the probability…

Answered: Let X be the number of packages being…

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...

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1. Let X be a random variable with PMF n px (k) = c( ½ )p³ for k = 0,1,..., n. k Find the value of c. Identify the distribution of X and find its mean and variance.
The marginal distributions of two random variables X and Y, together with some values of their joint distribution, are given in the table below. Fill in the table in such a way that X and Y are dependent random variables. Y=0 Y= 1 Y= 3 X=-1 0.06 0.60 X=3 0.04 0.40 0.50 0.10 0.40 1.00
2) A manufacturer has designed a process to produce pipes that are 10 feet long. The distribution of the pipe length, however, is actually Uniform on the interval 10 feet to 10.57 feet. Assume that the lengths of individual pipes produced by the process are independent. Let X and Y represent the lengths of two different pipes produced by the process. What is the probability that the second pipe (with length Y) is more than 0.35 feet longer than the first pipe (with length X)? Give your answer to four decimal places. Hint: Do not use calculus to get your answer.
4. A random sample of 6 items is drawn from a plant's daily production. Let the ran- r of good items and the number of defective dom variables X and Y denote the numbe items chosen, respectively. If the production contains 40 good and 10 defective items, find (a) the joint probability distribution function for X and Y. (b) the marginal distributions of X and y
Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.
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The marginal distributions of two random variables X and Y, together with some values of their joint distribution, are given in the table below. Fill in the table in such a way that X and Y are independent random variables. Y= 1 Y= 3 X= 0 0.50 X= 1 0.30 X= 2 0.10 0.10 0.20 0.50 0.50 1.00
The marginal distributions of two random variables X and Y, together with some values of their joint distribution, are given in the table below. Fill in the table in such a way that X and Y are independent random variables. Y= -2 Y= 0 Y= 3 X= -3 0.02 0.03 0.05 0.10 X=0 0.21 0.70 X= 3 0.06 0.20 0.20 0.30 0.50 1.00
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Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of u 1.3 parts (a) through (c) below. a. If 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3 kg during freshman year. The probability is (Round to four decimal places as needed.) b. If 16 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg. The probability is (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? OA. Since the weight gain exceeds 30, the distribution of sample means is a normal distribution for any sample size. OB. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size. and a standard deviation of a 5.1 kg. Complete OC. Since the…
The following table contains the probability distribution for the number of traffic accidents daily in a small town. Complete parts (a) through (c) below. Refer to chart below. Number of accidents daily (X) P(X=xi) 0 0.30 1 0.35 2 0.17 3 0.07 4 0.05 5 0.04 6 0.02 A.) Compute number of accidents a day B.) Complete standard deviation C.) What is the probability that there will be at least 2 accidents on a given day? Don't round

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