성균관대 응용통계1 시험족보.hwp

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 stu…