Statistics统计学作业代写 STAT 221代写

STAT 221(01) Spring 2019 Assignment Two

Due no later than 3:30 p.m. on Wednesday, April 17th, at the beginning of the class.

Statistics统计学作业代写 An urn initially contains r red balls and s black balls. A ball is selected at random but not removed and α balls of the same color

Problems  to  be graded :  Statistics统计学作业代写

1. A box contains 10 green balls, 6 black balls, and 14 red balls. Two balls are selected at random without replacement from the box. What is the probability that the first ball is red given that the second isred?
2. Suppose A, B, and C  are events  of strictly positive probability in some probability space.  If  P (A|C) >  P (B|C) and P (A|C^c) >  P (B|C^c), is it true that P (A) >  P (B)?  If P (A|C) >    P(A|C^c) and P (B|C) > P (B|C^c), is it true that P (A ∩ B|C) > P (A ∩ B|C^c)?
3. An urn initially contains r red balls and s black balls. A ball is selected at random but not removed and α balls of the same color as the selection are added to the urn. The process is then repeated with α balls of one color or the other added to the urn at each epoch. Witheach addition the population of the urn increases by α and it is helpful to imagine that the urn has unbounded capacity.

(a)What is the probability that the first ball selected was black given that the second ball selected wasblack?

(b)Showby mathematical induction that the probability of selecting a black ball in the kth drawing is invariant with respect to k.

4.Supposethat  Jaden  chooses  a  subset  S  of  size  s(0  ≤  s  ≤  n)  at .ranΣdom  from  the  set 

each of the  subsets of size s having probabilityof being chosen.

Suppose  that,  independently  of  Jaden,  Joanne  chooses  a  subset  T  of  size  t(0  ≤  t  ≤  n.) at random from the set,each of the subsets of size t having probability Statistics统计学作业代写

of being chosen. Let X be the number of elements in the set S ∩ T . Show that the p.m.f of X can be expressed in the three equivalent ways :

5. Suppose that X is a discrete random variable withg.f.

Compute Var(X) and E(Xe^X).

6. There are 10 students majoring statistics and 10 students not majoring statistics. They arerandomly split into 10 groups, with 2 students per group, which are all equally Let X be the number of groups consisting of 1 student majoring statistics and 1 student not majoring statistics. Find E(X).  Statistics统计学作业代写
7. Supposed that SK Wyverns and Doosan Bears play a “best of seven” Korean series, which means they play until one team wins four games. Assume Wyverns win every game indepen- dently with probability p. Let N be the number of games played. ComputeE(N ).
8. Suppose Jaden rolls a dice until he gets his first occurrence of “6” and then he stops. Let X denote the number of rolls until the first occurrence of “6”. Suppose Joanne flips a fair coin until she gets her first occurrence of “heads”  and then she stops.  Let Y  denote the number  of flips until the first occurrence of“heads”.

(a)FindE(X).

(b)FindVar(X).

(c)Find P (X ≥ Y).

Problems not to be graded :   Statistics统计学作业代写

1. Two boxes are placed in front of you. One box contains nine $1 bills and one $5 bill, while the other box contains two $1 bills and one $100 bill. You choose at random one of the two boxes and then two bills are randomly picked out of the chosen box. It appears that thesetwo bills are $1 bills. Next you get the opportunity to pick a third bill out of one of the two Should you stick to the chosen box or should you switch to the other box when you want to maximize the probability of picking the $100 bill?
2. Supposethat r different numbers are picked at random from the numbers 1, 2, 3, . . . , s. Let the random variable X be the sum of the r numbers picked. Find the expected value of X, E(X) and variance of X, Var(X).
3. Tenmarried couples are seated at random in a row of 20  Compute the expected number of wives that sit next to their husbands.   Statistics统计学作业代写
4. An elevator opens on the ground floor and N passengers enter it. Each passenger selects one floor (above the ground floor), and the elevator proceeds upward, stopping at each selected floor. Assume the following:
   • There are 10 floors above the ground
   • Each passenger selects one floor above the ground
   • Eachpassenger is equally likely to choose any of the 10
   • All passenger choices are
   • If no passenger enter, then the elevator makes zero

Find the expected number of stops that the elevator makes (not counting the ground floor).

更多代写：Python代码编写 Python代考推 英国essay代写被发现 传媒essay代写 英国essay代写范例 英国文献综述代写

合作平台：essay代写 论文代写 写手招聘 英国留学生代写