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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The manager of a stockroom in a factory has constructed the following probability distribution for thedaily demand (number of items used) for a particular tool. x 0 1 2 p(x) 0.1 0.5 0.4 It costs the factory P10 each time the tool is used.a. Find the mean and variance of the daily costs for the total usage of tools.b. Interpret the distribution based on its mean/ expected value
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To investigate the relation between hair color and eye color, the hair color and eye color of 5383 persons were recorded. The data are given in the following table: Hair Color ... Eye Color 1 2 Light 1168 825 305 Dark 573 1312 1200 a. Determine the joint and marginal probability distributions of X and Y. b. P(X + Y = 5) C. P(1 < Xs 3, 1
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following random 2. Let W be a random variable giving 1. Classify variables as discrete or continuous a. X: the number of automobile accidents per year in EDSA b. Y: the length of time to paly 18 holes of golf. c. M: the amount of eggs laid each month by a hen. d.P: the number of building permits issued each month in Camiling, the the number of heads minus the number of tails in three tosses of a coin. a. List all elements of the sample space S for the three tosses of the coin and to each sample point assign a value w of W. b. Find the probability distribution of the random variable W, assuming that the coin is biased so that a head is twice as likely Tarlac e. Q: the weight of grain produces per hectare. to occur as a tail. c. Compute for value, variance and standard deviation variabe W. the expected of the random
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