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?

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

Step-by-step 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}