2. An experiment consists of flipping a fair coin four times. Determine the frequency (mass)function and the cumulative distribution function of the following random variables:(a) The number of heads before the first tail.(b) The number of heads following the first tail.(c) The number of heads minus the number of tails.(d) The number of tails times the number of heads.

The PMF of a random variable i.e, discrete in nature. It gives the likelihood that the variable…

Answered: 2. An experiment consists of flipping a…

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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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.)
A baker is deciding how many batches of muffins to make to sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established a probability distribution. P(x) 1 0.15 2 0.35 3 0.40 4 0.10 Table 4.2 Define the random variable X.
ll 36 l 12% 7 15:04 4G .. Question One: (a) If 4 balanced coins are tossed simultaneously (or 1 balanced coin is tossed 4 times), compute the entire probability distribution and plot it. (b) Compute and plot the probability distribution for a sample of 5 items taken at random from a production process known to produce 30% defective items.
A company has seven applicants for two positions: three women and four men. Suppose that the seven applicants are equally qualified and that no preference is given for choosing either gender. Let x equal the number of women chosen to fill the two positions. (a) Write the formula for p(x), the probability distribution of x. (b) What are the mean ? and variance ?2 of this distribution? (Round your mean to one decimal place and your variance to two decimal places.)
Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail. 16 6 8 9 10 18 14 13 9 10 25 18 13 8 14 3 The sample mean is x = 12.1%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and σ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use ? = 0.01. (a) What is the level of significance? Compute the z value of the sample test statistic. (Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
Studies have shown that the percent of California Community College students that take a certain number of units per quarter follow the following distribution.
Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail. 15 7 7 13 13 20 13 12 5 10 26 22 13 7 11 3 The sample mean is x = 12.3%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and σ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use α = 0.01. (a) What is the level of significance? Compute the z value of the sample test statistic. (Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

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