Math 230 Final Exam
Part I. ShortAnswer Questions. Each of the following problems counts for 5 points.
Write your answers in the spaces ( ) provided after each question. You need not
show the work an
Math 230
(38) Clearly it is impossible to have X = Y = 1. In other words, the events
X = 1 and Y = 1 are mutually exclusive. Further, Z = 1 if and only
if X = 1 or Y = 1, i.e., Z = X Y , so pZ = pX Y
Math 230
(32) The marginal pmf pX1 (x1 ) is found by summing across the rows, while
pX2 (x2 ) is found by summing down the columns. Thus,
pX1 (0) = .01 + .02 + .03 + .02 = .08,
pX1 (1) = .04 + .36 + .
Math 230
(47) We let X be the height of a male chosen at random. So, X N (69, 2.82 )
using the N (, 2 ).
For (a), we are to nd P (65.5 < X < 74.6) (since X is a continuous
random whose density functio
Math 230
Solution to Assigned Problems 50, 51
(50) From the assumption that the lifetime, X ,(measured in years) of a
randomly selected component has an exponential distribution (with
1
parameter ), w
Math 230
(65) For the given data, and for H0 , H1 as given, the Pvalue is given by the
expression P [X 12.17] P Z 12.1712.1 = 1 P [Z < 1] = .1587.
.56/8
Thus, if population mean ll weight does not ex
MATH
(58) Given that cfw_X1 , . . . , X100 is a random sample drawn from Exp(),
1
one knows that for every i, = = . To get a onesided 95% C.I. on
, one sees from Central Limit Theorem that
from X
MATH
(55) In order to nd the level of condence involved for the interval (5.9, 6.7),
when a sample mean of 6.3 has been observed for a random sample of
size 81, we note the given interval has the form
Math 230
(24) From the table given for the pmf of X , we see that the possible values
of X are x = 2, x = 0, x = 4, x = 5. Therefore, the events X < 4
and X 0 are, respectively, equivalent to X = 2 X
Math 230
(19) If we let S be the event that the randomly chosen person is a smoker, and E be the event that
the randomly chosen person develops emphysema, then there are two things to note. The rst is
Math 230
Questions 1  3 all deal with a data set consisting of n = 7
items of bivariate numerical data, (xi , yi ), for i = 1, 2, , 7, whose
summary statistics are as follows:
xi = 136.5, y = 5.53428
Math 230
: 70
median: 75
1. (12 points) Given the following stemleaf plot for 40 sulfur dioxide emissions (x):
Tens
0
1
2
3





Ones
46
11123455555666777888999
00001222244466
0
(a) Fill in the
Math 230
Test 2
1. Suppose that X, Y are random variables with standard deviations x = 2; y = 3.
Let Z = 3X 2Y, and given that z = 6. Find the value for the covariance between X and Y,
namely Cov(X, Y
Math 230
1. (5 points) Let X have a standard normal distribution. Find the interval [d, d] such that
P(d X d) = 0.5.
Answer: ( d = 0.67 )
P(d X d) = 1 (P(X < d) + P(X > d), and, by symmetry, this is e
Math 230
(13) A students category is determined by the triple (x, y, z ), where x is the students gender, y is the
students standing, and z is the students college. There are two possibilities for x,
Math 230
Fall 2010
Solution to Assigned Problems 59  61
(59) Our observed value of p is
19
81
.2346 Thus, the 100(1 ) % con
dence interval will be given by .2346 z/2 (.2346)(.7654) .2346
81
.0471
Math 230
(70) It is false that the Pvalue is greater than .02; we reject H0 at level 2%
when the Pvalue is less than or equal to .02. This is exactly what is
meant by saying the result is statistica