Calculus For The Life Sciences
2nd Edition
ISBN: 9780321964038
Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher: Pearson Addison Wesley,
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 13.2, Problem 20E
To determine
(a)
To find:
The median of the random variable with the probability density function.
To determine
(b)
To find:
The probability that the random variable is between the expected value and the median.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
In the transmission of digital information, the probability that a bit has high, moderate, and low distortion is 0.01, 0.04, and 0.95, respectively. Suppose that three bits are transmitted and that the amount of distortion of each bit is assumed to be independent. Let X and Y denote the number of bits with high and moderate distortion out of the three, respectively. Determine: E(x) =
In the transmission of digital information, the probability that a bit has high, moderate, and low distortion is 0.01, 0.04, and 0.95,
respectively. Suppose that three bits are transmitted and that the amount of distortion of each bit is assumed to be independent.
Let X and Y denote the number of bits with high and moderate distortion out of the three, respectively. Determine:
(c) E(X)= i
Round your answer to two decimal places (e.g. 98.76).
Exercise 3. Let X be a random variable with mean µ and variance o². For a € R, consider the
expectation E((X − a)²).
a) Write E((X - a)²) in terms of a, μ and σ².
b) For which value a is E((X − a)²) minimal?
c) For the value a from part (b), what is E((X − a)²)?
Chapter 13 Solutions
Calculus For The Life Sciences
Ch. 13.1 - Repeat Example 1a for the function f(x)=2x2 on...Ch. 13.1 - Prob. 2YTCh. 13.1 - Prob. 3YTCh. 13.1 - Prob. 1ECh. 13.1 - Prob. 2ECh. 13.1 - Prob. 3ECh. 13.1 - Prob. 4ECh. 13.1 - Prob. 5ECh. 13.1 - Prob. 6ECh. 13.1 - Prob. 7E
Ch. 13.1 - Prob. 8ECh. 13.1 - Prob. 9ECh. 13.1 - Prob. 10ECh. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - Prob. 13ECh. 13.1 - Prob. 14ECh. 13.1 - Prob. 15ECh. 13.1 - Prob. 16ECh. 13.1 - Prob. 17ECh. 13.1 - Prob. 18ECh. 13.1 - Prob. 19ECh. 13.1 - Prob. 20ECh. 13.1 - Prob. 21ECh. 13.1 - Prob. 22ECh. 13.1 - Find the cumulative distribution function for the...Ch. 13.1 - Prob. 24ECh. 13.1 - Prob. 25ECh. 13.1 - Prob. 26ECh. 13.1 - Prob. 27ECh. 13.1 - Prob. 28ECh. 13.1 - Show that each function defined as follows is a...Ch. 13.1 - Prob. 30ECh. 13.1 - Show that each function defined as follows is a...Ch. 13.1 - Prob. 32ECh. 13.1 - Prob. 33ECh. 13.1 - Prob. 34ECh. 13.1 - Prob. 35ECh. 13.1 - Prob. 36ECh. 13.1 - Prob. 45ECh. 13.1 - Prob. 47ECh. 13.1 - Prob. 48ECh. 13.1 - Prob. 49ECh. 13.2 - YOUR TURN 1 Repeat Example 1 for the probability...Ch. 13.2 - Prob. 2YTCh. 13.2 - Prob. 3YTCh. 13.2 - In Exercises 1-8, a probability density function...Ch. 13.2 - Prob. 2ECh. 13.2 - Prob. 3ECh. 13.2 - Prob. 4ECh. 13.2 - Prob. 5ECh. 13.2 - Prob. 6ECh. 13.2 - Prob. 7ECh. 13.2 - Prob. 8ECh. 13.2 - Prob. 9ECh. 13.2 - Prob. 10ECh. 13.2 - Prob. 11ECh. 13.2 - Prob. 12ECh. 13.2 - Prob. 13ECh. 13.2 - Prob. 14ECh. 13.2 - Prob. 15ECh. 13.2 - Prob. 16ECh. 13.2 - Prob. 17ECh. 13.2 - Prob. 18ECh. 13.2 - Prob. 19ECh. 13.2 - Prob. 20ECh. 13.2 - Prob. 21ECh. 13.2 - Prob. 22ECh. 13.2 - Prob. 23ECh. 13.2 - Prob. 24ECh. 13.2 - Length of a leaf The length of a leaf on a tree is...Ch. 13.2 - Prob. 26ECh. 13.2 - Prob. 30ECh. 13.2 - Prob. 31ECh. 13.2 - Prob. 33ECh. 13.2 - Prob. 34ECh. 13.2 - Prob. 35ECh. 13.2 - Prob. 36ECh. 13.2 - Prob. 37ECh. 13.2 - Prob. 39ECh. 13.2 - Prob. 40ECh. 13.3 - YOUR TURN Repeat Example 2 for a flashlight...Ch. 13.3 - Prob. 1ECh. 13.3 - Prob. 2ECh. 13.3 - Prob. 3ECh. 13.3 - Prob. 4ECh. 13.3 - Prob. 5ECh. 13.3 - Prob. 6ECh. 13.3 - Prob. 7ECh. 13.3 - Prob. 8ECh. 13.3 - Prob. 9ECh. 13.3 - Prob. 10ECh. 13.3 - Prob. 11ECh. 13.3 - Prob. 12ECh. 13.3 - Prob. 13ECh. 13.3 - Prob. 14ECh. 13.3 - Describe the standard normal distribution. What...Ch. 13.3 - Prob. 16ECh. 13.3 - Suppose a random variable X has the Poisson...Ch. 13.3 - Prob. 19ECh. 13.3 - Prob. 20ECh. 13.3 - Prob. 21ECh. 13.3 - Prob. 22ECh. 13.3 - Prob. 23ECh. 13.3 - Find each of the following probabilities for the...Ch. 13.3 - Prob. 25ECh. 13.3 - Prob. 26ECh. 13.3 - Prob. 27ECh. 13.3 - Prob. 28ECh. 13.3 - Prob. 30ECh. 13.3 - Determine the cumulative distribution function for...Ch. 13.3 - Prob. 36ECh. 13.3 - Prob. 37ECh. 13.3 - Prob. 38ECh. 13.3 - Prob. 39ECh. 13.3 - Pygmy Height The average height of a member of a...Ch. 13.3 - Prob. 41ECh. 13.3 - Prob. 42ECh. 13.3 - Prob. 43ECh. 13.3 - Prob. 44ECh. 13.3 - Prob. 45ECh. 13.3 - Prob. 46ECh. 13.3 - Prob. 47ECh. 13.3 - Prob. 48ECh. 13.3 - Prob. 49ECh. 13.3 - Earthquakes The proportion of the times in days...Ch. 13.3 - Prob. 51ECh. 13.3 - Prob. 52ECh. 13.3 - Prob. 53ECh. 13.3 - Prob. 54ECh. 13.3 - Prob. 55ECh. 13.3 - Printer Failure The lifetime of a printer costing...Ch. 13.3 - Electronic Device The time to failure of a...Ch. 13.CR - Prob. 1CRCh. 13.CR - Prob. 3CRCh. 13.CR - Prob. 4CRCh. 13.CR - Prob. 5CRCh. 13.CR - Prob. 6CRCh. 13.CR - Prob. 7CRCh. 13.CR - Prob. 8CRCh. 13.CR - Prob. 9CRCh. 13.CR - Prob. 10CRCh. 13.CR - Prob. 11CRCh. 13.CR - Prob. 12CRCh. 13.CR - Prob. 13CRCh. 13.CR - Prob. 14CRCh. 13.CR - Prob. 15CRCh. 13.CR - Prob. 16CRCh. 13.CR - Prob. 17CRCh. 13.CR - Prob. 18CRCh. 13.CR - Prob. 19CRCh. 13.CR - Prob. 20CRCh. 13.CR - Prob. 21CRCh. 13.CR - Prob. 22CRCh. 13.CR - Prob. 23CRCh. 13.CR - Prob. 24CRCh. 13.CR - Prob. 25CRCh. 13.CR - Prob. 26CRCh. 13.CR - Prob. 27CRCh. 13.CR - Prob. 28CRCh. 13.CR - Prob. 29CRCh. 13.CR - Prob. 30CRCh. 13.CR - Prob. 31CRCh. 13.CR - Prob. 32CRCh. 13.CR - Prob. 33CRCh. 13.CR - Prob. 34CRCh. 13.CR - Prob. 35CRCh. 13.CR - Prob. 36CRCh. 13.CR - Prob. 39CRCh. 13.CR - Prob. 40CRCh. 13.CR - Prob. 41CRCh. 13.CR - Prob. 42CRCh. 13.CR - Prob. 43CRCh. 13.CR - Prob. 44CRCh. 13.CR - Prob. 45CRCh. 13.CR - Prob. 46CRCh. 13.CR - Prob. 47CRCh. 13.CR - Prob. 48CRCh. 13.CR - Prob. 52CRCh. 13.CR - Prob. 54CRCh. 13.CR - Prob. 55CRCh. 13.CR - Prob. 56CRCh. 13.CR - Prob. 57CRCh. 13.CR - Prob. 58CRCh. 13.CR - Prob. 59CRCh. 13.CR - Prob. 60CRCh. 13.CR - Prob. 61CRCh. 13.CR - Yeast cells The famous statistician William...Ch. 13.CR - Prob. 65CRCh. 13.CR - Equipment Insurance A piece of equipment is being...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- Assume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.arrow_forwardF(x) is cdf of X. Cumulative probability X is 2,4,7 and 9 is 0.1,0.4,0.8 and 1. calculate the probability if more than fivearrow_forwardJust d,earrow_forward
- (Math 161A/163 review) Suppose that X₁, X2, X3 are independent Exponential (A) random variables. A> 0 and r> 0 are constants. Find the mean and variance of Y where Y = 2(X₁+rX2 - X3)arrow_forwardEstimate the probability that a missile fired at speed x = 350 knots will hit the target.arrow_forwardWhen a man observed a sobriety checkpoint conducted by a police department, he saw 660 drivers were screened and 6 were arrested for driving while intoxicated. Based on those results, we can estimate that P(W) = 0.00909, where W denotes the event of screening a driver and getting someone who is intoxicated. What does P (W) denote, and what is its value? C What does P (W) represent? OA. P (W) denotes the probability of driver being intoxicated. B. P (W) O C. P (W) denotes the probability of screening a driver and finding that he or she is not intoxicated. denotes the probability of screening a driver and finding that he or she is intoxicated. OD. P (W) denotes the probability of a driver passing through the sobriety checkpoint. P(W) = (Round to five decimal places as needed.) when a man observed a sobriety checkpoint conducted by a por intoxicated. Based on those results, we can estimate that P(W) = intoxicated. What does P (W) denote, and what is its value? What does P (W) represent?…arrow_forward
- Harrison is a sports statistician and is interested in the number of strikeouts by a starting pitcher over the past five years for a certain professional baseball league. He randomly selects 471 games and records the number of strikeouts by one of the starting pitchers in the game, where the pitcher for the home or visiting team is selected at random. Harrison records the total number of strikeouts by the starting pitcher in that game, x, and the probability of each value, P(x), as shown in the table provided. Find the mean and the standard deviation of the probability distribution using a TI-83, TI-83 Plus, or TI-84 graphing calculator. Round the mean and standard deviation to three decimal places. Number of strikeouts x P(x)0 0.0161 0.0452 0.0593 0.0834 0.0985…arrow_forwardThe probability of the closing of the ith relay in the circuits shown is given by pi. Let P₁= 0.6, P2=0.1, pa=0.5, pa=0.7, Ps= 0.3. If all relays function independently, what is the probability P that a current flows between A and B for the respective circuits? (b) (a) P= 0.1167 (b) P 0.5156 e Barrow_forwardDetermine the value of k such that this will be a probability mass function for X = 17, 19, 21, 23: k = P[X = 21] = F(19) = Mean = Standard Deviation = f(x) (decimal form). = 4x - 13 k (decimal form).arrow_forward
- In information theory (the mathematical study of communication systems, which figures prominently in electrical engineering), the information (or entropy) of a discrete and finite random variable X is defined as: H(X)= E[log2(1/P(X))] where p(.) is the PMF for X. Answer the following: 1. Assume that the set of values that X can take is {x1, ..., xn} and p(x;) > 0 for all i. Derive an expression for H(X) in terms of p(x1), ..., p(xn). 2. Assume that n = 2. What values of p(x1) and p(x2) maximize H(X)?arrow_forwardWhen a man observed a sobriety checkpoint conducted by a police department, he saw 667 drivers were screened and 4 were arrested for driving while intoxicated. Based on those results, we can estimate that P(W) = 0.00600, where W denotes the event of screening a driver and getting someone who is intoxicated. What does P (W) denote, and what is its value? What does P(W) represent? O A. P(W) denotes the probability of a driver passing through the sobriety checkpoint. O B. P(W) denotes the probability of driver being intoxicated. O C. P(W) denotes the probability of screening a driver and finding that he or she is not intoxicated. O D. P(W) denotes the probability of screening a driver and finding that he or she is intoxicated. P(W) =O (Round to five decimal places as needed.)arrow_forwardLet X be the random variable with the probability distribution function shown in Table 9.1.A: Find the value of E[g(X)], where g(X)=(−2X+3)(Correct upto 2 decimal points).arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Continuous Probability Distributions - Basic Introduction; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=QxqxdQ_g2uw;License: Standard YouTube License, CC-BY
Probability Density Function (p.d.f.) Finding k (Part 1) | ExamSolutions; Author: ExamSolutions;https://www.youtube.com/watch?v=RsuS2ehsTDM;License: Standard YouTube License, CC-BY
Find the value of k so that the Function is a Probability Density Function; Author: The Math Sorcerer;https://www.youtube.com/watch?v=QqoCZWrVnbA;License: Standard Youtube License