Question

An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (o) which we write hth, int, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is hu, then r (11)=2. Suppose that the random variable x is defined in terms of r as follows: X-6R-2R2-3. The values of x are thus: Outcome h ht|th ththhhttthhth htt Value of ΧΙ "1111-31-3111 Calculate the probability distribution function of x, i.e. the function px (x). First, fill in the first row with the values of x. Then fill in the appropriate probabilities in the second row. Value x of x 0 0 00 5 ?

Answer 1

COR Total output =8 Number of counts foo X=1 = 6 = P(X=1) = 6 =0 Number of counts foo xe - > X=-3) = Yalue x ofx I Br22 60100

Answer 2

An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (

h

) and "tails" (

t

) which we write 

hth

, 

ttt

, etc. For each outcome, let 

R

 be the random variable counting the number of heads in each outcome. For example, if the outcome is 

hht

, then 

=Rhht2

. Suppose that the random variable 

X

 is defined in terms of 

R

 as follows: 

=X−R1

. The values of 

X

 are given in the table below.

Outcome	hhh	hth	ttt	thh	hht	tht	tth	htt
Value of  X	2	1	−1	1	1	0	0	0

Calculate the values of the probability distribution function of 

X

, i.e. the function 

pX

. First, fill in the first row with the values of 

X

. Then fill in the appropriate probabilities in the second row.