1. A drawer contains 4 purple socks and 6 orange socks. You reach in and randoml

Question

1. A drawer contains 4 purple socks and 6 orange socks. You reach in and randomly grab a sock, then repeat the process until you have removed all 10 socks from the drawer. Define indicator v ariables x. 1 ifthe ith sock is purple otherwise if the ith sock is orange otherwise 1 a) Define (in words) five different random variables, different from X1, X2,.X10, and , ½, , Y10 whose values are determined by the outcome of this random experiment. Make sure at least one of the random variables you define is an indicator random variable. Note that there are many possible random variables; you only need to define five. b) List the possible values of each random variable you define. c) What is the relationship between Xi and Y for a given value of i? d) Express each of your random variable from part (a) in terms of X,X2,, X0. If your random variable cannot be expressed in this way, explain why not.

Explanation / Answer

(a)

A = 2 if ith sock is purple else 0

B = 3 if ith sock is purple else 0

C= 4 if ith sock is purple else 0

D = 5 if ith sock is purple else 0

E= 1 if ith sock is purple else 0

(b)

A can have 2 or 0,

B can have 3 or 0,

C  can have 4 or 0,

D can have 5 or 0,

E can have 1 or 0,

(c)

Xi and Yi always have sum equal to 1 for any value of i because a sock will either be purple or orange, so either Xi will be 1 and Yi be 0 OR Xi will be 0 and Yi be 1

(d) Ai= 2*Xi

Bi = 3*Xi

Ci= 4*Xi

Di= 5*Xi

SO, if X1=1 , A1 will be 2 , X1=0, A1=0

if X1= 1, B1 will be 3 , X1=0, B1=0

and so on

Ei= Xi

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.