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성균관대 응용통계1 시험족보.hwp

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응용통계 I
Midterm I, 2010 10 29

READ THE INSTRUCTIONS BEFORE BEGINNING THE EXAM!
1 Show all your work!
2. Only A4 crib sheet, pencil and erasers are allowed!
3. Do not consult with others(includes all possible cheating means)!
4. Good Luck!
1. Let X1 and X2 be independent, exponentially distributed random variables with the same parameter , so that X1 and X2 have joint pdf


for x1 ` 0 and x2 ` 0 and f(x1,x2) = 0 for other values of x1 and x2.

Find the distribution of Y = X1 - X...

응용통계 I
Midterm I, 2xxx 10 29

READ THE INSTRUCTIONS BEFORE BEGINNING THE EXAM!
1 Show all your work!
2. Only A4 crib sheet, pencil and erasers are allowed!
3. Do not consult with others(includes all possible cheating means)!
4. Good Luck!
1. Let X1 and X2 be independent, exponentially distributed random variables with the same parameter , so that X1 and X2 have joint pdf


for x1 ` 0 and x2 ` 0 and f(x1,x2) = 0 for other values of x1 and x2.

Find the distribution of Y = X1 - X2 and Z = X1 / X2. Are Y and Z
are independent(20pts)

2. A family has n children with probability αpn,(n≥1) where α≤1-p/p.

(a) What proportion of families have more than three children(10pts)

(b) If each child is equally likely to be a boy or girl(independent of other children), what proportion of families consist of k boys (and any number of girls)(10pts)
Hint: For part b) consider the case k=0 separately.
3. In SKKU SME community, it is found that 60% of the students of…(생략(省略)) all students taking Engineering Certification(EC) track oppose an increase in increasing the credits for BSM in EC program while 80% of the students not in EC track favor the increasing. If 65% of all the student who voted are in EC track, what proportion of the voted students are favored in increasing credits for BSM(15pts)

4. Give a careful definition of an appropriate sample space and the number of possible outcomes for each of the following games for (a) (b) and (c). For (d), the number of possible ranges is asked. (20pts)
(a) A balanced coin is tossed until three heads appeared.
(b) A balanced die is rolled until an ace appears.
(c) Three distinct cards are selected sequentially from a standard deck of 48 Korean hwatoo.
(d) The annual rain falls in Natural Science Campus of SKKU.

5. Suppose that the random variable X has a continuous distribution with the following pdf:

Determine the value x0 such that F(x0) = 0.8(15pts)

6. Suppose that the random variable X ha

다.

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