Question

Suppose you flip a coin twice and count the number of heads you observe. Youthen roll a 4 sided die (like a 6 sided die, but only has values 1 through 4). If therandom variableYis the number of heads you’ve observed multiplied by the vauleof your die roll, what is the sample space ofY?

Answer 1

Sample space=S={HH1,HT1,TH1,HH2,HT2,TH2,HH3,HT3,TH3,HH4,HT4,TH4}

Explanation:

The sample space for Y can be made as under

Coin is tossed two times={HH,HT,TH,TT}

4-sided die is rolled={1,2,3,4}

Coin is tossed two times and 4-sided die is rolled

={HH1,HT1,TH1,TT1,HH2,HT2,TH2,TT2,HH3,HT3,TH3,TT3,HH4,HT4,TH4,TT4}

Y be the random variable that the number of heads observed multiply by die roll number so, the sample space for Y would be

Sample space=S={HH1,HT1,TH1,HH2,HT2,TH2,HH3,HT3,TH3,HH4,HT4,TH4}