Concept explainers
Repeat Example 2 if the probability density function is
Life Expectancy The life expectancy (in hours) for a particular brand of lightbulb is a continuous random variable with probability density function
(A) What is the average life expectancy of one of these lighlbulbs?
(B) What is the probability that a bulb will last longer than this average?
Want to see the full answer?
Check out a sample textbook solutionChapter 11 Solutions
EP CALCULUS F/BUS.,ECON.-BRIEF-ACCESS
- Repeat Example 1a for the function f(x)=2x2 on [1,2]. What is the probability that X will be between 32 and 2?arrow_forwardShow that each function defined as follows is a probability density function on the given interval; then the indicated probabilities. f(x)=12(1+x)3/2;[0,) a. P(0X2) b. P(1X3) c. P(X5)arrow_forwardShow that each function defined as follows is a probability density function on the given interval; then find the indicated probabilities. f(x)=(1/2)ex/2;[0,) a. P(0X1) b. P(1X3) c. P(X2)arrow_forward
- Eastern Hemlock Ring shake, which is the separation of the wood between growth rings, is a serious problem in hemlock trees. Researchers have developed the following function that estimates the probability P that a given hemlock tree has ring shake: P(A,B,D)=11+e3.680.016A0.77B0.12D where A is the age of the tree yr, B is 1 if bird pecking is present and 0 otherwise, and D is the diameter in. of the tree at breast height. Source: Forest Products Journal. a. Estimate the probability that a 150-year-old tree with bird pecking present and a breast height diameter of 20in., will have ring shake. b. Estimate the probability that a 150-year-old tree, with no presence of bird pecking and a breast height diameter of 20in., will have ring shake. c. Develop a statement about what can be said about the influence have on the probability of ring shake. d. Using the total differential, estimate the probability if the actual age of the tree was 160 years and the diameter at breast height was 25in., Assume that no bird pecking was present. Compare your answer to the actual value. Hint: Assume that B=0 and exclude that variable from your calculations e. Comment on the practicality of using differentials in part d.arrow_forwardFind the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill