Let X ~ Hypergeometric (4, 3, 4). The random experiment defining X can be described as follows: from a bag with 4 blue marbles and 3 red marbles, we draw 4 marbles without replacement, and count the number of blue marbles drawn. ) Give the PMF of X. Some possibly-useful numbers: Px (0) Px(1) Px (2) Px(3) Give the conditional PMFs of (X | X is even) and (X | X is odd). Pxx is even (0) Pxx is even (2) PxX is even (4) = 35, (7) = 35, (8) Px(4) Compute E[X | X is even] and E[X | X is odd]. = 70. Pxx is odd (1) Pxx is o (3)

If the RVSX1, X2,..., X, all have n .2 the same variance s and he correlation oxil ficient between each pair (X;, X;), i # jof them is p, show that the correlation coefficient 2n between -1 X; and Li=n+1 X; is %3D1 пр 1+(n-1)p

Let R=2Ei] ={ a+ib:g,bEZ,;=5-} %3D is aring ?

Consider a random sample X1,...,Xn,... ∼ iid Beta(θ,1) for n > 2. Prove that the MLE and UMVUE are both consistent estimators for θI got MLE = n/-∑logXi and UMVUE = (n-1)/∑logXi. Need help in proving consistency

A recent study claims that using music in a class enhances concentration and consequently helps students absorb more information. A researcherdecided to test this claim on a smaller group of randomly selected students from three different classes. Each classroom was provided with a different environment for students to study. Classroom A had constant music being played in the background, classroom B had variable music being played and classroom C was a regular class with no music playing. After one month, the researcher conducted a test for all the three groups and ranked their scores. What statistical test would be most appropriate for testing the research hypothesis? Explain your answer.

Suppose X is a discrete random variable. Let the pmf of X be equal to 5 - x f(x) = x = 1,2,3,4 10 Find the cdf of X, that is F(X).

a and b working together can do a given job in 4 days, b and c together can do the job in 3 days, and a and c together can do it in 2.4 days. in how many days can they finish the job all together?    Answer is 7 days. Please show your solution.

A study of fox rabies in a country gave the following information about different regions and the occurrence of rabies in each region. A random sample of  n1 = 16  locations in region I gave the following information about the number of cases of fox rabies near that location. x1:    Region I Data 1 9 9 9 7 8 8 1 3 3 3 2 5 1 4 6 A second random sample of  n2 = 15  locations in region II gave the following information about the number of cases of fox rabies near that location. x2:    Region II Data 1 1 5 1 6 8 5 4 4 4 2 2 5 6 9   What is the value of the sample test statistic? (Test the difference μ1 − μ2. Do not use rounded values. Round your final answer to three decimal places.)

Two teachers had 30 of their students take a test. Teacher A found a mean of 78.6 with a SD-3.5 while teacher B found a mean of 77.3 and a SD-4.1. At the 97% level, test the opnion that class B is less than class A. 1. Is the test (A-Left Tailed, B-Right Tailed, C-2-Tailed) (separate with a comma if there are 2) 2. Critical Value 3. Test statistic 4. 3-decimal p-Value

Directions: Solve the given problem. Show your solutions. Of all the registered automobiles in Colorado, 8% fail the state emissions test. Twelve automobiles are elected at random to undergo an emissions test. a. Find the probability that exactly four of them fail the test. b. Find the probability that fewer than four of them fail the test. c. Find the probability that more than three of them fail the test.