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Consider the random variable

`x`

following a discrete probability distribution taking values

`0,1,2,cdots,9`

, each with probability

`(1)/(10)`

. Then i) calculate the probability that

`x`

is between 3 and 7 (both inclusive). ii) calculate the mean and variance of

`x`

. iii) calculate the mean

`Y`

where

`Y=x(x+1)`

.