5. Let X be a random variable with distribution function

 

Plot the graph of F(x) and then evaluate E(x).

a. Based on these 100 observations, is a Poisson distribution with a mean of 2.4 an appropriate model? Perform a goodness-of-fit test with α=0.05.

b. Perform the test using P-value approach.

a. Do the data suggest that the two methods provide the same mean value for natural vibration frequency? Using the P-value approach.

b. Find a 95% confidence interval on the mean difference between the two methods and use it to answer the question in part (a).

6. There are two classes of Probability and Statistics course. The problems of the final exam are identical for the two classes. Let μ₁ and μ₂ denote the population means of scores of class A and class B, respectively, and σ₁ and σ₂ denote the population variances of scores of class A and class B, respectively. A random sample of 13 students are taken from class A and 11 students are taken from class B. The sample average and standard deviation of scores of each class are class A: X̄ₐ = 84, Sₐ = 4 and class B: X̄բ = 77, Sբ = 6. Test whether the population means of scores of the two classes are equal. Make assumptions if necessary.

a. What is the probability function of Y?

b. What is the cumulative distribution function of Y?

c. Find the mean and variance of X.

a. What is the fitted linear regression model?

b. What is the coefficient of determination of this model?