Problem 7. Show the following:(1) Suppose that X and Y are independent random variables. Show that V(X - Y) = V(X) +V(Y).(2) Let X and Y be the number on a ticket in two subsequent draws with replacement from aopaque box with 20 tickets numbered by {1,2,..., 20}. Use Chebyshev's inequality to find anumber e such thatP(|XY|

Question 1:For independent random variables X and Y, V(X-Y) = V(X) + V(Y). This means that the…

Answered: Problem 7. Show the following: (1)…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A teacher believes that students who study more than four hours for her tests will do better than students who do not study for her tests. To test this belief, the teacher recruited 16 students and randomly assigned them to two groups: G1: a group of n1=8 students that studied more than four hours for her test, and G2: a group of n2=8 students that did not study for her test. The following are the data from G1, who studied more than four hours for the test: n1=8 M1=85 s1=5 (this is the standard deviation of the sample, dividing the sum of squares by n1) The following are the data from G2, who did not study for the test: n2=8 M2=75 s2=4 (this is the standard deviation of the sample, dividing the sum of squares by n2) Perform a t-test by answering the questions below. Use an alpha-level of α=.05. 0. Using formulas from Section 4, compute the estimates of the population variances, est. σ12 and est. σ22 (from s1 and s2 above). 1. What is the research…
4. (4.1-8). In a smoking survey among men between the ages of 25 and 30. 63% prefer to date nonsmokers, 13% prefer to date smokers, and 24% dont care. Suppose nine such men are selected randomly. Let X equal the number who prefer to date nonsmokers and Y equal the number who prefer to date smokers. (a) Determine the joint pmf of X and Y. Be sure to include the support of the pmf. (b) Find the marginal pmf of X. Again include the support.
Could you please give the correct solutions for this homework
1. On the basis of her experience with clients, a clinical psychologist thinks that depression may affect sleep. She decides to test this idea. The sleep of nine depressed patients and eight normal controls is monitored for three consecutive nights. The average number of hours slept by each subject during the last two nights is shown in the following table: (Pagano, 2010). If proved significant, compute of the effect size. Hours of Sleep Depressed patients 7.1 Normal controls 8.2 6.8 7.5 6.7 7.3 7.7 7.8 7.5 8.0 6.2 7.4 6.9 7.3 6.5 6.5 7.2
3b)
- 7. A class has 30 students. If there are 20 boiys and two students are selected at random calculate the probability that one is a girl and one is a boy m no giris are selected
1.A family wishes to adopt 4 pets from a total of 13 dogs and 7 cats available at an animal shelter. The variable "x" being measured is the number of dogs. Show the probability distribution table, using 3 columns: one for x, one for P(x), and one for x*P(x). The second column should show calculations using C(Dt). 2. A student forum at a high school needs to elect 5 people from 10 Grade 11 students and 15 Grade 12 students who are available. The variable"" being measured is the number of Grade 12 students. Show the probability distribution table, using 3 columns: one for x, one for P(x), and one for x*P(x). The second column should show calculations involving C(Dt).
3. An integer is randomly chosen from the set 1, 2,..., 100. If this integer is divisible by 2 we let Y = 0, and if it is not divisible by 2 but is divisible by 3 then Y = 1. We let Y = 2 in all other cases. Find mean and variance of Y.
3a)
1. Given that X~N(39,32)A Random variable X is normally distributed and has a mean of 9 C Random variable X is not normally distributed and the mean is 39 B Random variable X is normally distributed and has a mean of 3 D Random variable X is normally distributed and the mean is 39

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