Let X1, X2, · · · , Xn be a random sample from a population with probability mass function f(x) =    θ x = −1 2θ x = 0 1 − 3θ x = 1 , where θ is an unknown parameter satisfying 0 ≤ θ ≤ 1/3. (a) Find the method of moments estimator of θ. (b) Is the method of moments estimator an unbiased estimator of θ?

14 pointslet x be the seats in the small van and y the seats in the large van. how many seats does the large van have? a company uses two vans to transport worker from a free parking lot to the workplace between 7: 00 and 9: 00a. m. one van has 9 more seats than the other. the smaller van makes two trips every morning while the larger one makes only one trip. the two vans can transport 69 people, maximum. how many seats does the larger van have?

When you have 25 numbers, and jake picks 3 random numbers and puts them back, what is the chance bob has of picking those 3 numbers when he picks 6 random numbers (without putting them back)? explain.

Solve each quadratic equation by factoring and using the zero product property. x^2 + 18x = 9x