Question

Let W be a random variable giving the number of heads minus the number of tails in three tosses of a coin. List the elements of the sample space S for the three tosses of the coin and to each sample point assign a value w of W.

Answer 1

Answer:

HHH, W = 3-0 = 3

HHT, W= 2-1=1

HTH, W= 2-1=1

THH, W=2-1 =1

HTT, W= 1-2=-1

THT, W= 1-2=-1

TTH, W=1-2=-1

TTT, W=0-3 = -3

So then the sample space for W is:

$S= [-3,-1,1,3]$

Just 4 possible values from 8 possible combinations for the 3 random tosses

Step-by-step explanation:

For this case we define W as the random variable who represent the number of heads minus the number of tails in three tosses of a coin.

W= # heads- # coins

Since we toss a coin 3 times we have 2*2*2= 8 possible results. We can list the results and the corresponding values for W like this:

HHH, W = 3-0 = 3

HHT, W= 2-1=1

HTH, W= 2-1=1

THH, W=2-1 =1

HTT, W= 1-2=-1

THT, W= 1-2=-1

TTH, W=1-2=-1

TTT, W=0-3 = -3

So then the sample space for W is:

$S= [-3,-1,1,3]$

Just 4 possible values from 8 possible combinations for the 3 random tosses