space.discussion.Homework+2

​Homework 2 (Problems) (GWU EMSE-271)
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 * Problem 1: Airline Booking**
 * PMF problem (Slides 33-36); start by graphing data?
 * How would you graph in Minitab? Excel?
 * Part a. Sum of the probability that 45,46, 47, 48, 49, and 50 people show up.
 * Etc.
 * Hint?: The probability that the first standby will get on depends on the average of the people how normally show up (expected value).
 * Class Notes: P<50) for a, ticketed passengers.


 * Problem 2: Upright Freezer**
 * Expectation (mean) (E[X]) and Variance (V[X]) problem for a function with 3 discrete values.
 * (Looking for point estimates an variance. See slides 57-61?)
 * Part a: Slide 40 for E[X]. Not liking the values I am getting for V[X]. Must be computing E[X**2] and E[X] **2
 * Using the formulas after the Defintion for variance at the top of Sldie 42 gave me an answer that I liked bettter for V[X]. Not sure what to do for E[X**2] and E[X] **2; not sure I am understanding the notation correctly.
 * Part b: See slide 41.
 * Part c:
 * Part d Substitution again.
 * Class Notes: a2. Read correctly to get E[X]2. b. Look up formula on slide. d. Substitute in, not linear. Could do in table (like solution).

Discussion: Does E[h(x)] = h(E[X]), only if h(x) is of form ax +b.

Problem 3: k out-of n
 * Estimator distribution choice problem. Need to look at Slide 46 or 47.
 * Brings out problems with this slide last time: Which distribution do you choose for which kind of (word) problem. How do you compute E[X] and V[X] for them data given. By example, what is n and what is p for the binomial.
 * Need to work and expand lecture notes on distributions more.
 * [|Wikipeida]: Binomial: "It is frequently used to model number of successes in a sample of size //n// from a population of size //N."//
 * For this particular problem, can use Binomial and Excel to solve.
 * Class Notes: Need to add 3 of 5, 4 of 5, and 5 of 5, or like Van Dorp take (1- Pr(x<=2). Know binomial because like coin toss. Can check the three required assumptions. (Strictly <2, but because discrete, <= 2)

Problem 4: Steel Shafts
 * Like calcuating probabilites slide 50 or 51?
 * Note: Binomial Poisson when N is large and p<.1. Binomila  Normal when np>5 and np(1-p) > 5.
 * Draw pictures.
 * Class Notes: Still got wrong answers. Using normal, OK, but old approach. With Excel, could just use Binomial. In working the normal approach, stay with Binomial as long as possible. Pr(x .. ) then switch to Normal Pr(y ... ). Use Normdist function. Look at C, for discrete variable, 15 is in the range.

Problem 5: Concrete Beams**
 * Words Point Estimate are throughout problem. See slides 57-61.
 * HINT: Can check calcuations in Minitab.
 * Problem 5 going better than problem 4. Challenge for me is stating the estimator, not making as much sense as I would like. Slides 60-61 name unbiased estimators. Look at thise pages again with respect to stating the estimator for this problem.
 * Solving for V[X] helped me a little with problem 2a. I put the data into an Excel worksheet and added things up. Did not have to. He has given us the values we need to compute the answers to the question.
 * Class Notes: What we are here to learn to do. Inference. Talking about biased versus unbiased estimators. Slide 50 and 58, 59. Want estimator closest to mean and with smallest level of uncertainty. V[X] is biased. S[X] is unbiased, V is sum over n. S is Sum over (n-1). If V[X] is biased, is and why the Std. Deviation is biased or not, square root is not linear (h(x) example.