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(Solved): Answers for R studio - so language R \# 1. I roll a fair dice two times. Let the random variable X b ...
Answers for R studio - so language R
\# 1. I roll a fair dice two times. Let the random variable be the maximum of the \# two numbers rolled, and let the random variable be the difference of the two numbers \# (larger value minus smaller value). \# a. Calculate and graph the probability mass function of . Calculate the Expected value of and its variance.| b. Calculate and graph the probability mass function of . Plot it. Calculate the Expected value of and its variance.
Expert Answer
a. To calculate the probability mass function of X, we need to consider all possible outcomes of rolling a dice two times. There are six possible outcomes for each roll, so the total number of outcomes is 6 x 6 = 36.The maximum of the two numbers rolled can take the values 1, 2, 3, 4, 5, or 6. The probability of getting a particular value of X is the probability that both rolls are less than or equal to X, minus the probability that both rolls are less than or equal to X-1 (since X is the maximum of the two numbers rolled). So, we can calculate the probability mass function of X as follows: