The probability experiment is to roll a pair of fair, labeled dice. Refer to the

Question

The probability experiment is to roll a pair of fair, labeled dice. Refer to the sample space involving two dice that is discussed in the chapter 3 handouts under COURSE DOCUMENTS in blackboard. Compute the following probabilities: P(product of the pips is at most 6) P(sum of the pips is at least 10) P(sum of the pips is exactly 7) P(product of the pips is a odd number) P(product of the pips is a multiple of 6) P(sum of the pips is at least 2) Refer to sample space in problem (1). Let Q = pips on die 1 + pips on die 2. For instance, if you rolled a (3,4), then Q would take on the value of 3 + 4 = 7. Or, if you rolled a (2,6), then Q would take on the value of 2 + 6 = 8. The chapter 4 handouts under COURSE DOCUMENTS in blackboard might prove very useful here. Construct a discrete probability distribution for the random variable, Q and show that it satisfies the two properties of a discrete probability distribution. Compute the theoretical mean, µ, of the discrete random variable Q. Compute the theoretical standard deviation, , of the discrete random variable Q.

Explanation / Answer

sample space (s) =

(6,6)

product is at most 6 =  

Probability = 11/36

sum of the pips is at least 10 =

(4,6) , (5,5), (5,6) , (6,5), (6,6)

probability = 5/36

sum is exactly 7 = (1,6), (2,5) , (3,4), (4,3) , (5,2) , (6,1)

probability = 6/36 = 1/6

P [sum is atleast 2] = 1- P[ sum is less than 2 ] = 1-0 = 1

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5)

(6,6)

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