# docenti.luiss.it

## Solution to  the appello of June 28   Stat17Exam2SOL.pdf

### Section 9.5.1  is a bit tricky, and  you do not have to learn it. Also, we did not do Section 7.6, 8.3.1, and we ignored the t distribution in general. Also, we did not use the continuity correction which appears on Section 7.5 and also later. You can ignore it. In some problems in the book, ignoring it may give you a result which is somewhat different than the book’s. We did not discuss Value At Risk (VAR) which appears in Section 6.6 in an exercise, so ignore it.

Here are some old exams. The style is not exactly the same, but it gives you some ideas and exercises to try.  This year we did not study for Question A of Stat16Fin1A and for  part 5 of stat15, and question E in stat14.      Stat13Fin1Sol       Stat14FinSol     (1)     Stat15Fin2SSol    Stat16Fin1ASol

Prediction in regression: If you want to predict an outcome of a certain investment $\dpi{300}\inline x_0$ then the prediction is  $\dpi{300}\inline \widehat \alpha + \widehat \beta x_0$ .  If you want to provide a confidence interval for the predicted outcome, that is, a prediction interval,  use the formula $\dpi{300}\inline \widehat \alpha + \widehat \beta x_0$  $\dpi{300}\inline \pm$ $\dpi{300}\inline z_{\alpha/2} W$  for a prediction interval with confidence 100($\dpi{300}\inline 1-\alpha$). For example, take $\dpi{300}\inline z_{\alpha/2}$=1.96 for a 95% interval. Remember, we don’t use the t table.  See page 573 in the book for the formula of W, which was  explained in class on May 2.

Some solutions to problems from Chapter 5  Solutions

## Some comments on expectation, click :Expectaion

### Here is a histogram of the quiz2 grades. I inserted zero for those who did not take the quiz.  HistQuiz2

Percentiles (also known as quantiles):  we use the definition in Ross:

To find the sample 100p percentile of a data set of size n
1. Arrange the data in increasing order.
2. If np is not an integer, determine the smallest integer greater than np. The data value in that position is the sample 100p percentile.
3. If np is an integer, then the average of the values in positions np and np + 1 is the sample 100p percentile.

Example: if n=4 and the data is 2,5,6,9,  and p=0.25   (the 0.25 percentile is also called the first  quartile) then np is an integer.  According to item 3 above,  the first quartile is (2+5)/2.   Note that any number t  in [2,5] satisfies that at least 1/4 of the data are ≤ t and at least 3/4 are ≥ t.  We take the middle of the interval.

If n=5,  and the data is 2,5,6,9,11, then the quartile is  5.

# This is the normal density. There is a misprint in the book on on page 267.

## Normal Table:  Table-Norm

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