3 votes 3 votes A fair die is rolled thrice and the random variable X records the number of different outcomes that result. For example, if two 6's and one 3's are rolled, then X records two different outcomes. What is the variance of X? Mathematical Logic probability + – Avdhesh Singh Rana asked Jan 14, 2018 recategorized Jan 15, 2018 by Avdhesh Singh Rana Avdhesh Singh Rana 630 views answer comment Share Follow See all 17 Comments See all 17 17 Comments reply joshi_nitish commented Jan 14, 2018 reply Follow Share is it 0.3048 ? 1 votes 1 votes saxena0612 commented Jan 14, 2018 i edited by saxena0612 Jan 15, 2018 reply Follow Share I am also getting $0.3048$ $0$ $1$ $2$ $\frac{6}{216}$ $\frac{90}{216}$ $\frac{120}{216}$ [Edit] : This one is correct : Reason $\{1,1,1\}$ = $1$ distinct outcome . $1$ $2$ $3$ $\frac{6}{216}$ $\frac{90}{216}$ $\frac{120}{216}$ $\frac{1446}{216}-(\frac{546}{216})^2=0.304783 \approx0.3048$ 1 votes 1 votes joshi_nitish commented Jan 14, 2018 reply Follow Share @Saxena 0.3058 ? 0 votes 0 votes saxena0612 commented Jan 14, 2018 reply Follow Share Typo!! 0 votes 0 votes Avdhesh Singh Rana commented Jan 14, 2018 reply Follow Share saxena0612 If you can explain solution a little bit more. 0 votes 0 votes Aditya Tewari commented Jan 14, 2018 reply Follow Share focus on "number of different outcomes" one will be where all are same eg.(6,6,6) second where any 2 are same and another is diff...eg (1,1,2) third where all 3 are diff. eg.(4,5,6) 0 votes 0 votes Manu Thakur commented Jan 15, 2018 reply Follow Share @Aditya when all dice are same like 4,4,4 will it be called 0-different (or) 1-different outcome? 0 votes 0 votes joshi_nitish commented Jan 15, 2018 reply Follow Share @Manu, according to language of qsn, qsn means to say distinct outcomes 0 votes 0 votes Avdhesh Singh Rana commented Jan 15, 2018 reply Follow Share It will count as one different outcome. 0 votes 0 votes Manu Thakur commented Jan 15, 2018 reply Follow Share Variance = $E(x^2) - (E(X))^2$, yes, but, i am not getting answer as 0.3048. 0 votes 0 votes joshi_nitish commented Jan 15, 2018 reply Follow Share ${\color{Red}{red}}$ literals are correct 0 votes 0 votes Manu Thakur commented Jan 15, 2018 reply Follow Share red are the ones put by me in the pic of @saxena0612 but still i am not getting the answer 0.3048 may be i am making some calculations mistake 0 votes 0 votes Manu Thakur commented Jan 15, 2018 reply Follow Share thanks @nitish, i got the answer. 1 votes 1 votes saxena0612 commented Jan 15, 2018 reply Follow Share @Manu,@Nitish : May be i interpreted it wrong but please correct me ! $\{6,6,3\}=2$ different outcome because $\{3,6\}$ because this is set right.Now $\{1,1,1\}$or $\{2,2,2\}$ will be $1$ is it? 0 votes 0 votes Anu007 commented Jan 15, 2018 reply Follow Share Yes {1,1,1} = 1 different outcome {1,2,2} = 2 different outcome {1,2,3} 3 different outcome. 1 votes 1 votes saxena0612 commented Jan 15, 2018 reply Follow Share @ Anu007 I am still not satisfied i think $\{1,1,1\}$ should be $0$ its called $'0'$ different outcome $\Rightarrow$ similiar outcome whereas $\{1,1,1\}='1'$ does not make any sense of being called as $'1'$ different outcome. Maybe some one give better clarification. 0 votes 0 votes Anu007 commented Jan 15, 2018 reply Follow Share X records two different outcomes says how many distinct outcome are there. ex: {6,6,3} = 2 so with {1,1,1} = 1 distinct outcome. 1 votes 1 votes Please log in or register to add a comment.