5.Application: Suppose that a population consists of only 5 members and the values of Y are as follows.MemberY2Define the probability distribution of Y. Compute for u (or E(Y)) and o? (or Var (Y)).If a sample size of 3 is taken from the population through random sampling, how many wayscan we select a sample?Enumerate all possible outcomes of a random sampling of size 3 (in a table). For eachoutcome, compute for the sample mean (Y) and sample variance (S).Note: No need to show the solution of your computations.a.b.C.Find the probability distribution of Y (i.e., the sampling distribution). By looking at the table(or graph), determine if the distribution is symmetric or asymmetric (i.e., skewed to the leftor skewed to the right).d.Compute for E(Y) and Var (Y)Verify that Y is an unbiased estimator of u.e.f.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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2c)
Suppose that we have a sample space S = {E1, E2, E3, E4, E5, E6, E7}, where E1, E2, ...E7 denote the sample points. The following probability assignments apply: P(E1) = 0.05, P(E2) = 0.20, P(E3) = 0.20, P(E4) = 0.25, P(E5) = 0.15, P(E6) = 0.10, and P(E7) = .05. Let A = {E1, E4, E6}, B = {E2, E4, E7}, C = {E2, E3, E5, E7}a) Find the P(A), P(B) and P(C), write the answers on the space provided. b) Find B' and P(B')c) Find A U B and P(A U B)
Suppose X and Y are uncorrelated random variables. Which of the following statements are true? Group of answer choices: the sample correlation for 10 data points sampled from the joint distribution of X and Y will be exactly 0. X and Y have no relationship X and Y are independent X and Y have no linear relationship
9.) At the Wimbledon Tennis Championship, to win a match in men’s singles a player must win the best of five sets. The following data represent the number of sets played, X, in the men’s singles final match for the years 1968 to 2011. X 3 4 5 Frequency 19 12 13 (a) Construct a probability model for the random variable, X, the number of sets played in the Wimbledon men’s singles final match.(b) Draw a probability histogram.(c) Compute the mean and standard deviation of the random variable X.
The Census Bureau gives this distribution for the number of people in American households in 2016. Family size 1 2 4 6. 7 Proportion 0.28 0.35 0.15 0.13 0.06 0.02 0.01 Note: In this table, 7 actually represents households of size 7 or greater. But for purposes of this exercise, assume that it means only households of size exactly 7. Suppose you take a random sample of 4000 American households. About how many of these households will be of size 2? Sizes 3 to 7? The number of households of size 2 is about The number of households of size 3 to 7 is about
3.) In an experiment on the behavior of young children, each subject is placed in an area with 5 toys. Past experiments have shown that the probability distribution of the number X of toys played with by a randomly selected subject is as follows. Number of Toys Probability 2 3 4 5 0.03 0.16 0.30 0.23 0.17 a.) Find the P(X = 5). b.) If a subject is chosen at random, what is the probability they played with more than 2 toys? c.) If a subject is chosen at random, what is the probability they played with less than 3 toys? d.) Find the expected number of toys played with. e.) Find the standard deviation of the number of toys played with.
C. A population consists of five numbers 1, 2, 3, 4, and 5. Consider samples of size 3 that can be drawn from this population. a. List all the possible samples and the corresponding mean SAMPLE MEAN 1 2 4 5 6 7 8 9 10 b. Construct the sampling distribution of the sample means find the mean Sampling Distribution of Sample Means Sample Mean (X) Probability P(X) Frequency X• P(X) 1 2 3 4 Hx = EX • P(X) = 6. So, the mean of the sampling distribution of the sample means is 7 9 10 c. Find the variance of the sampling distribution of the sample means P(X) X-u (X -µ)² P(X) • (X - 4)? 1 2 3 (o?2) = EP(X) • (X – )° %3D 6. 8 So, the variance of the 9. sampling distribution is 10
Part I: Sections 1.1 - 1.5 4. A flower garden has 40 flowers: 10 yellow, 5 white, 8 red, and 17 pink. Assume that 3 flowers are randomly selected. If the sampling is done with replacement, what is the (a) probability that the first two flowers are pink and the last flower is yellow? (b) probability that at least one of the flowers is red? If the sampling is done without replacement, what is the
Q1. The table below shows voters choose at random between African American and African American democrats: Republican Democrats Total African-American 4 12 16 White/others 44 40 84 Total 48 52 100 Using the above table find the probability that the voter is either African American or Democrat
I need help with part a-c
4 Define the random variable, its distribution, and compute for the variable/measure that is being asked. You can follow the example below
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).

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