Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of X is as follows.X1 23 4p(x) 0.2 0.10.4 0.3(a) Consider a random sample of size n = 2 (two customers), and let X be the sample mean number of packages shipped. Obtain the probability distribution of X.11.5P(X) 0.040.040.1722.533.50.20.22.240.094(b) Refer to part (a) and calculate P(X ≤ 2.5).0.45=(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 thedistribution of R. [Hint: Calculate the value of R for each outcome and use the probabilities from part (a).]R0123P(R) 0.30.360.220.12(d) If a random sample of size n = 4 is selected, what is P(X ≤ 1.5)? [Hint: You should not have to list all possible outcomes, only those for which x ≤ 1.5.]0.0045×

Given the distribution of X is : x1234P(x)0.20.10.40.3

Answered: Let X be the number of packages being…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let Y be a random variable with the following probability distribution: p(y) = y/6 for y = 1; 2; 3 and (0 otherwise). Write the probability distribution for Y in the form of a table. Find E(Y), V(Y), and E(Y 3 − 1).
Use the probability distribution to complete parts (a) and (b) below. The number of defects per 1000 machine parts inspected Defects 1 2 4 Probability 0.264 0.290 0.240 0.148 0.042 0.016 ..... (a) Find the mean, variance, and standard deviation of the probability distribution.
The probability distribution of the number of students absent on Mondays, is as follows: X O 1 2 3 4567 f(x) 0.02 0.03 0.26 0.34 0.22 0.08 0.04 0.01 (a) What is the probability that more than 3 students are absent. (b) Compute the expected value of the random variable X. Interpret this expected value. (c) Compute the variance and standard deviation of the random variable X. (d) Compute the expected value and variance of Y : (e) Compute the covariance Cov(X, Y) = 7X+ 3. (f) What is the value of the ratio Cov(X,Y)/Var(X) ? (g) What is the value of Cov(X, Y)/Var(X) for Y = ß0 + ß₁X ? (For this exrcise, you can use excel. No need to show all calculations, just specify the formulas and present the final values.) (a) (b) (c) (d) (e) (f) (g)
Use the probability distribution to complete parts (a) and (b) below. The number of defects per 1000 machine parts inspected 3 Defects 1 4. Probability 0.262 0.299 0.233 0.153 0.037 0.016 ... (a) Find the mean, variance, and standard deviation of the probability distribution. The mean is (Round to one decimal place as needed.)
Use the probability distribution to complete parts (a) and (b) below. The number of defects per 1000 machine parts inspected Defects 1 2 3 4 5 Probability 0.259 0.293 0.244 0.150 0.037 0.017 ... (a) Find the mean, variance, and standard deviation of the probability distribution. The mean is (Round to one decimal place as needed.) The variance is (Round to one decimal place as needed.) The standard deviation is (Round to one decimal place as needed.) (b) Interpret the results. The mean is , so the average batch of 1000 machine parts has The standard deviation is so the typical number of defects in a batch of 1000 (Round to one decimal place as needed.)
The probability distribution of random variable X is defined as follows: X 0 1 2 3 4 Probability 0 0.3 0.1 0.3 0.3 Find the expected value and the standard deviation of X.
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Use the probability distribution to complete parts (a) and (b) below. The number of defects per 1000 machine parts inspected Defects 1 4 Probability 0.262 0.299 0.233 0.153 0.037 0.016 ... (a) Find the mean, variance, and standard deviation of the probability distribution. The mean is 1.5. (Round to one decimal place as needed.) The variance is (Round to one decimal place as needed.)
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Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of X is as follows: x 1 2 3 4 p(x) 0.4 0.3 0.2 0.1 a. Consider a random sample of size n = 2 (two customers), and let x̄ be the sample mean a number of packages shipped. Obtain the probability distribution of x̄. b. Refer topart (a) and calculate P( x̄ ≤ 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. [ Hint Calculate the value of R for each outcome and use the probabilities from part (a).) d. If a random sample of size n= 4 is selected, what is P( x̄≤ 1.5)? [ Hint You should not have to list all possible outcomes, only those for which x̄ ≤ 1.5.)
An appliance dealer sells three different models of upright freezers having 11.5, 14.9, and 20.1 cubic feet of storage space. Let x = the amount of storage space purchased by the next customer to buy a freezer. Suppose that x has the following probability distribution. X p(x) 11.5 14.9 20.1 0.2 0.5 0.3 (a) Calculate the mean (in cubic feet) of x. cubic feet Calculate the standard deviation (in cubic feet) of x. (Round your answer to three decimal places.) cubic feet (b) If the price of the freezer depends on the size of the storage space, x, such that Price = 25x8.5, what is the mean price paid (in dollars) by the next customer? $ (c) What is the standard deviation of the price paid (in dollars)? (Round your answer to the nearest cent.) $

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