Concept explainers
a.
To write: All the eight possible arrangements for the boy and girl child.
To find: The
a.

Answer to Problem 12.48E
The eight possible arrangements for the boy and girl child are given below,
The probability to get first two girls and a boy is
Explanation of Solution
Given info:
A couple has planned to have three child, eight possible arrangements for the girl and boy are possible. All these eight arrangements are equally likely to occurrence.
Justification:
Sample space:
The sample space is defined as the set of all possible outcomes from an experiment.
The total number of possible outcomes is,
A couple plans to have three children. One of the possible combinations to have three children is “Girl, Girl or Boy”. Similarly, the other possible combinations can be obtained.
All the eight possible arrangements for the boy and girl child are the sample space S which is given below:
Where, G represents the girl child and B represents the boy child.
Calculation:
Equally likely events:
An
Since, the eight possible arrangements are equally likely to occur. The probability for one of the eight possible arrangements is calculated as follows:
Thus, the probability for getting any one from the eight possible arrangements is
b.
To find: The probability that
b.

Answer to Problem 12.48E
The probability that the couple have two girl children is
Explanation of Solution
Given info:
Assume that X denotes the number of girls that the couple has.
Calculation:
Let the number of girls X that the couple has equals to 2 girls.
The outcomes for 2 girls are
The probability that the couple have two girl children is calculated as follows:
Thus, the probability that the couple have two girl children is
c.
To find: The values of X and the probability distribution for X.
c.

Answer to Problem 12.48E
The values taken by X are 0, 1, 2, and 3.
The probability distribution is given below:
X | 0 | 1 | 2 | 3 |
Probability |
Explanation of Solution
Calculation:
Random variable:
The random variable is a variable which has numerical values or outcomes obtained from a random experiment.
Finite Probability Model:
A probability model with a finite sample space is called the finite probability model.
Assigning probabilities to the finite probability model:
- List all the probabilities for all individual outcomes.
- These probabilities should lie between 0 and 1 and the total sum of all probabilities exactly equal to 1.
- The probability for occurrence of any event is the sum of individual probabilities of that event.
Values of X:
The random variable X takes values 0, 1, 2, 3 because the couple has planned to have 3 children and X denotes the number of girl child. So, the possible number of girl child the couple can have is 0, 1, 2, and 3.
Probability distribution for X:
Let the number of girls X that the couple has equals to 0. The possible outcome is
The probability to have no girl child is calculated as follows:
Thus, the probability to have no girl child is
Let the number of girls X that the couple has equals 1. The possible outcomes are
The probability to have 1 girl child is calculated as follows:
Thus, the probability to have one girl child is
Let the number of girls X that the couple has equals 2. The outcomes for 2 girls are
The probability to have 2 girl children is calculated as follows:
Thus, the probability to have two girl child is
Let the number of girls X that the couple has equals 3. The possible outcome is
The probability to have 3 girl children is calculated as follows:
Thus, the probability to have three girl child is
The probability distribution is given below:
X | 0 | 1 | 2 | 3 |
Probability |
Want to see more full solutions like this?
Chapter 12 Solutions
BASIC PRACTICE OF STATISTICS >C<
- The PDF of an amplitude X of a Gaussian signal x(t) is given by:arrow_forwardThe PDF of a random variable X is given by the equation in the picture.arrow_forwardFor a binary asymmetric channel with Py|X(0|1) = 0.1 and Py|X(1|0) = 0.2; PX(0) = 0.4 isthe probability of a bit of “0” being transmitted. X is the transmitted digit, and Y is the received digit.a. Find the values of Py(0) and Py(1).b. What is the probability that only 0s will be received for a sequence of 10 digits transmitted?c. What is the probability that 8 1s and 2 0s will be received for the same sequence of 10 digits?d. What is the probability that at least 5 0s will be received for the same sequence of 10 digits?arrow_forward
- V2 360 Step down + I₁ = I2 10KVA 120V 10KVA 1₂ = 360-120 or 2nd Ratio's V₂ m 120 Ratio= 360 √2 H I2 I, + I2 120arrow_forwardQ2. [20 points] An amplitude X of a Gaussian signal x(t) has a mean value of 2 and an RMS value of √(10), i.e. square root of 10. Determine the PDF of x(t).arrow_forwardIn a network with 12 links, one of the links has failed. The failed link is randomlylocated. An electrical engineer tests the links one by one until the failed link is found.a. What is the probability that the engineer will find the failed link in the first test?b. What is the probability that the engineer will find the failed link in five tests?Note: You should assume that for Part b, the five tests are done consecutively.arrow_forward
- Problem 3. Pricing a multi-stock option the Margrabe formula The purpose of this problem is to price a swap option in a 2-stock model, similarly as what we did in the example in the lectures. We consider a two-dimensional Brownian motion given by W₁ = (W(¹), W(2)) on a probability space (Q, F,P). Two stock prices are modeled by the following equations: dX = dY₁ = X₁ (rdt+ rdt+0₁dW!) (²)), Y₁ (rdt+dW+0zdW!"), with Xo xo and Yo =yo. This corresponds to the multi-stock model studied in class, but with notation (X+, Y₁) instead of (S(1), S(2)). Given the model above, the measure P is already the risk-neutral measure (Both stocks have rate of return r). We write σ = 0₁+0%. We consider a swap option, which gives you the right, at time T, to exchange one share of X for one share of Y. That is, the option has payoff F=(Yr-XT). (a) We first assume that r = 0 (for questions (a)-(f)). Write an explicit expression for the process Xt. Reminder before proceeding to question (b): Girsanov's theorem…arrow_forwardProblem 1. Multi-stock model We consider a 2-stock model similar to the one studied in class. Namely, we consider = S(1) S(2) = S(¹) exp (σ1B(1) + (M1 - 0/1 ) S(²) exp (02B(2) + (H₂- M2 where (B(¹) ) +20 and (B(2) ) +≥o are two Brownian motions, with t≥0 Cov (B(¹), B(2)) = p min{t, s}. " The purpose of this problem is to prove that there indeed exists a 2-dimensional Brownian motion (W+)+20 (W(1), W(2))+20 such that = S(1) S(2) = = S(¹) exp (011W(¹) + (μ₁ - 01/1) t) 롱) S(²) exp (021W (1) + 022W(2) + (112 - 03/01/12) t). where σ11, 21, 22 are constants to be determined (as functions of σ1, σ2, p). Hint: The constants will follow the formulas developed in the lectures. (a) To show existence of (Ŵ+), first write the expression for both W. (¹) and W (2) functions of (B(1), B(²)). as (b) Using the formulas obtained in (a), show that the process (WA) is actually a 2- dimensional standard Brownian motion (i.e. show that each component is normal, with mean 0, variance t, and that their…arrow_forwardThe scores of 8 students on the midterm exam and final exam were as follows. Student Midterm Final Anderson 98 89 Bailey 88 74 Cruz 87 97 DeSana 85 79 Erickson 85 94 Francis 83 71 Gray 74 98 Harris 70 91 Find the value of the (Spearman's) rank correlation coefficient test statistic that would be used to test the claim of no correlation between midterm score and final exam score. Round your answer to 3 places after the decimal point, if necessary. Test statistic: rs =arrow_forward
- Business discussarrow_forwardBusiness discussarrow_forwardI just need to know why this is wrong below: What is the test statistic W? W=5 (incorrect) and What is the p-value of this test? (p-value < 0.001-- incorrect) Use the Wilcoxon signed rank test to test the hypothesis that the median number of pages in the statistics books in the library from which the sample was taken is 400. A sample of 12 statistics books have the following numbers of pages pages 127 217 486 132 397 297 396 327 292 256 358 272 What is the sum of the negative ranks (W-)? 75 What is the sum of the positive ranks (W+)? 5What type of test is this? two tailedWhat is the test statistic W? 5 These are the critical values for a 1-tailed Wilcoxon Signed Rank test for n=12 Alpha Level 0.001 0.005 0.01 0.025 0.05 0.1 0.2 Critical Value 75 70 68 64 60 56 50 What is the p-value for this test? p-value < 0.001arrow_forward
- 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





