Determine the correlation for the following joint probability distribution 1 1 2 4 3 4 5 7 fw(X.y) 1/8 1/4 1/2 1/8
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- 1. A random variable x has the probability distribution as follows: 1. 2 3. 4 P(x) 1/15 k/15 k/5 4/15 k/15 a. Find k. b. Construct a probability histogram to descibe P(x).5.1.1 WP X 1.0 1.5 1.5 2.5 3.0 y 1 23+ 4 5 fxy(x, y) 1/4 1/8 1/4 1/4 1/8 5.2.2 WP Consider the joint distribution in Exercise 5.1.1. Determine the following: a. Conditional probability distribution of Y given that X = 1.5 b. Conditional probability distribution of X that Y = 2 c. E(Y | X = 1.5) d. Are X and Y independent?(CO 3) Consider the following table of hours worked by part-time employees. These employees must work in 5 hour blocks. Weekly hours worked 5 15 20 25 Find the mean of this variable. 17.50 16.80 12.20 18.95 Probability 0.06 0.61 0.18 0.15
- Find the mean and variance of the following probability distributions.The following six graphs correspond to three probability density functions and their cu- mulative distribution functions, but they are all mixed up. 0.8 1.5 0.6 A. В. 0.4 0.5 0.2 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 1.5 0.8 0.6 C. D. 0.4- 0.5 0.2 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 0.8 0.6 E. F. 2 0.4 0.2 0.2 0.4 0.6 0.8 0.2 0.4 0,6 0.8 Identify the graphs for each of the three probability density functions (PDFS), in alphabetical order. For each PDF, indicate which graph represents the corresponding cumulative distribution funetion (CDF). PDF CDF4:48 Mid-Statistics Exam First Semester (Sta.. Section 5. Arrivals of customers at a check counter follow a uniform distribution. It is known that, during a given 30- minute period, one customer arrived at the counter. Find the probability that the customer arrived during the last 5 minutes of the 30- minute period? * (2/2 Points) 0.0333 0.2000 0.0500 0.0300 0.1666 v None of the Above Activity Chat Teams Assignments More More Edit
- I. Which of the following are discrete probability distributions? (Yes or No) 1. 3 4 5 P(x) 0.10 0.20 0.25 0.40 0.05 2. 3 4 P(x) 0,05 0.25 0,33 0.28 0,08 3. 4 5 P(x) 0.08 0.25 0.34 0.31 0,04 4. 2 3 4 5 P(x) 0.03 0.22 1.01 0.23 0.02 5. 3 4 5 P(x) 0.05 0.27 0.34 0.28 0.06 6. 2 3 4 5 P(x) 1 3 3 10 10 10 7. 3. 4 P(x) 15 15 8. 2 4 5 6 P(x) 4. 25 25 25 25 9. 3 4 P(x) 1. 3. 20 20 1 10 10 10. 1 3 4 P(x) 0.212 0.113 0.125 0.224 0.306 -5.22 a. Form the probability distribution table for P(x) = , for x = 1,, 2, 3. %3D b. Find the extensions xP(x) and x²P(x) for each x. Find E[xP(x)] and E[x*P(x)]. d. Find the mean for P(x) = , for x = 1, 2, 3. 2 e. Find the variance for P(x) =, for x = 1, 2, 3. 6' f. Find the standard deviation for P(x) = *, for o 62 aluvilidsdon х%3D 1, 2, 3.3. Fill in the blank spaces of table B1 using information compiled in table B. Table B Breusch-Godfrey Serial Correlation LM Test: Prob. F(2,55) Prob. Chi-Square(2) F-statistic 11.70006 0.0001 Obs*R-squared 17.90823 0.0001 Table B1: Breusch-Godfrey Serial Correlation LM Test F-statistic: Probability: a. Write down the null and alternative hypotheses underlying Breusch-Godfrey serial correlation (autocorrelation) test. b. Will you accept or reject the null hypothesis based on the Breusch-Godfrey test for residual autocorrelation? Why or why not?
