Answered: Suppose I have an unfair coin, it lands…

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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Question

Suppose I have an unfair coin, it lands on heads 75% of the time. If I flip this coin four times, what is the probability that I will get only 1 heads? What is the mean for number of heads? Variance? Standard Deviation?

2. During my office hours (from 12pm to 6pm), an average of about 1 student per hour comes in for help. Assuming that the probability of a student coming in is uniform throughout my office hours, what are the odds that on a particular day I would have 6 students come in for help? What is the mean number of students that will come see me on a particular day? Variance? Standard deviation?

3. The average bmi (body mass index) of 500 college students is normally distributed with a mean of 25, with a standard deviation of 5. (A) How many students have a bmi between 22 and 29? (B) How many students have a bmi of more than 29? (C) How many students have a bmi of less than 22? (D) What level of bmi would put you in the bottom 10% of the weight distribution? Top 10%?

4. Suppose you have a sample of 5 people where X represents cookie consumption in the past week. the following X: (6, 5, 4, 1, 1). What is the mean of X? What is the Standard deviation of X? What is the Standard Error of X? Calculate the 95% confidence interval for X. Calculate the 99% confidence interval for X. Interpret your findings.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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