Question: 11. [3 points] Answer the following questions:a. Write down the probability distribution for the result of a single roll of a fair six-sideddie. Compute the

11. [3 points] Answer the following questions:a. Write down the probability distribution for the result of a single roll of a fair six-sideddie. Compute the mean and standard deviation of this distribution.b. Compute the mean and standard deviation of the probability distribution given intextbook problem 6.2.c. Which has the higher mean: the distribution in part a (which could be thought of asthe maximum of a single die), or the distribution in problem 6.2 (the maximum oftwo dice)? Which distribution has the higher standard deviation?d. e maximum of 50 die rolls also has a probability distribution. e possible valuesare the integers 1 through 6, and each one of these values has a positive probability.You do not need to compute this probability distribution, but consider its mean andstandard deviation. Do you think the mean of this distribution will be larger, smaller,or the same as the mean in part b)? Do you think the standard deviation will be larger,smaller, or the same as the standard deviation in part b? Explain the reasoning behindyour answers.

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