
Concept explainers
To find: that the statement is true or false: two events that are not mutually exclusive must be independent, justify answer.

Answer to Problem 7.58E
False
Explanation of Solution
Independent
Independent event means if there is no affects on the probability of the other event occurring.
Disjoint or mutually exclusive event
The events cannot occur at the same time called as disjoint or mutually exclusive.
Example
Suppose A is the event of tossing heads and B the event of tossing heads at least once.
So there two events are dependent or not independent, because if tossed heads at least once. Then there would be more likely to have tossed heads twice
The events are not disjoint; researcher can toss heads twice and heads at least once at the same time.
Chapter 7 Solutions
Statistics Through Applications
Additional Math Textbook Solutions
Elementary Statistics (13th Edition)
Thinking Mathematically (6th Edition)
A First Course in Probability (10th Edition)
Precalculus
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Elementary Statistics: Picturing the World (7th Edition)
- Please help me with this question on statisticsarrow_forwardPlease help me with this statistics questionarrow_forwardPlease help me with the following statistics questionFor question (e), the options are:Assuming that the null hypothesis is (false/true), the probability of (other populations of 150/other samples of 150/equal to/more data/greater than) will result in (stronger evidence against the null hypothesis than the current data/stronger evidence in support of the null hypothesis than the current data/rejecting the null hypothesis/failing to reject the null hypothesis) is __.arrow_forward
- Please help me with the following question on statisticsFor question (e), the drop down options are: (From this data/The census/From this population of data), one can infer that the mean/average octane rating is (less than/equal to/greater than) __. (use one decimal in your answer).arrow_forwardHelp me on the following question on statisticsarrow_forward3. [15] The joint PDF of RVS X and Y is given by fx.x(x,y) = { x) = { c(x + { c(x+y³), 0, 0≤x≤ 1,0≤ y ≤1 otherwise where c is a constant. (a) Find the value of c. (b) Find P(0 ≤ X ≤,arrow_forwardNeed help pleasearrow_forward7. [10] Suppose that Xi, i = 1,..., 5, are independent normal random variables, where X1, X2 and X3 have the same distribution N(1, 2) and X4 and X5 have the same distribution N(-1, 1). Let (a) Find V(X5 - X3). 1 = √(x1 + x2) — — (Xx3 + x4 + X5). (b) Find the distribution of Y. (c) Find Cov(X2 - X1, Y). -arrow_forward1. [10] Suppose that X ~N(-2, 4). Let Y = 3X-1. (a) Find the distribution of Y. Show your work. (b) Find P(-8< Y < 15) by using the CDF, (2), of the standard normal distribu- tion. (c) Find the 0.05th right-tail percentage point (i.e., the 0.95th quantile) of the distri- bution of Y.arrow_forward6. [10] Let X, Y and Z be random variables. Suppose that E(X) = E(Y) = 1, E(Z) = 2, V(X) = 1, V(Y) = V(Z) = 4, Cov(X,Y) = -1, Cov(X, Z) = 0.5, and Cov(Y, Z) = -2. 2 (a) Find V(XY+2Z). (b) Find Cov(-x+2Y+Z, -Y-2Z).arrow_forward1. [10] Suppose that X ~N(-2, 4). Let Y = 3X-1. (a) Find the distribution of Y. Show your work. (b) Find P(-8< Y < 15) by using the CDF, (2), of the standard normal distribu- tion. (c) Find the 0.05th right-tail percentage point (i.e., the 0.95th quantile) of the distri- bution of Y.arrow_forward== 4. [10] Let X be a RV. Suppose that E[X(X-1)] = 3 and E(X) = 2. (a) Find E[(4-2X)²]. (b) Find V(-3x+1).arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman





