Chapter 4，HW＝Discrete Random Variable ＂h，catsyxy，momewtork Answer the following questuons besed on the conter below， Six offeren colored dice are roled，of interest is the number of dice thas show a twh， 9．In wrods，detine the rendom variable\％， A．How many dice are folled 8 The number of dure that show a 1 vio e The color of the dire D．The oncome of the roll of the ares b．List the values that 7 may take on， A \( y=1,3,8 \) \％いい \( 3 \quad y=0,1,2 \ldots 1,8 \) c \( x=1,2 \) мルノ， 6 D \( Y=2,1,0_{1}, \ldots \) C，CVE the disuributan ofy， A \( Y=B\left(7, \frac{1}{7}\right) \) \( 81 / 2=B\left(6, \frac{1}{7}\right) \) \( e x=13\left(7, \frac{1}{6}\right) \)

When rolling six colored dice, the random variable of interest is the number of dice that show a specific face, say a "two." This type of random variable is classified as a discrete random variable because it can only take on specific integer values based on the outcome of the dice rolls, such as 0, 1, 2, up to 6 twos shown across the rolled dice. In the realm of probability and statistics, the distribution of our random variable can be modeled using the binomial distribution. Since there are six trials (the number of dice rolled) and the probability of rolling a two on each die is \(1/6\), we can say the random variable follows a \(Y \sim B(6, \frac{1}{6})\) distribution, indicating that we're looking at a scenario with multiple independent Bernoulli trials.