Answered: The change in depth of a river from one…

The change in depth of a river from one day to the next, measured (in feet) at a specific location, is a random variable Y with the following density function: fG) = } - 3

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

2.4
The change in depth of a river from one day to the next, measured (in feet) at a specific
location, is a random variable Y with the following density function:
fG) = {6
-3<y<3,
elsewhere.
2.4.1. What type of distribution does Y follow?
2.4.2. Find E (Y)
2.5
Y has a density function
(2 – y), 0 < y S 2
f(v)
elsewhere
Find the mean and variance of Y.
2.6
Given that the moment-generating function for the chi-square random variable is derived by
m(t) = (1– 2t) . Differentiate this mgf to find the mean and variance of the chi-square
distribution.

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Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 50 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that ? = 7.20 ml/kg for the distribution of blood plasma. (d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.50 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.) ______ male firefighters
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