22. A 12-sided die is characterized by a Uniform probability distribution over t

Question

22. A 12-sided die is characterized by a Uniform probability distribution over the numbers 1-12. The mean and the standard deviation of a roll of this die is: a. 6.5,11.92 b. 12.0,1.00 c. 6.0,3.45 d. 6.5,3.45 e. None of the above 23. Students arrive at Baker's office hours according to a Poisson distribution with parameter 3.8 (that is, 3.8 arrivals per hour). What are the mean and standard deviation of the number of students coming to Baker's office? a. 3.8,3.8 c. 3.8,14.4 d. 3.8,1.9 e. None of the above

Explanation / Answer

For a uniform distribution with end points a and b, the mean is given as (a+b)/2 and the variance is given as (b-a)2/12

In this case a=1 and b=12

thus mean is (1+12)/2=6.5

Variance is (12-1)2/12 =10.083

standard deviation is sqaure root of variance which is sqrt(10.083)=3.175

Thus none of the options is correct. option is E

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