Answer :

As success is considered when we get an odd number when we roll a die.


As die is rolled twice , so we can get no success or a single success or we can get odd both the times an odd number.


If X is the random variable denoting the success then X can take value 0,1 or 2


P(getting an odd number in a single rolling of die) = 3/6 = 1/2


As rolling a die is an independent event:


P(getting an odd on first roll and probability of getting odd on second roll)=P(getting an odd on first roll) x P(getting an odd on second roll)


Note: P(AՈB) = P(A)P(B) where A and B are independent events.


P(X=0) = P(even number on first throw) x P(even on second throw)


=


P(X=1) = P(even number on first throw) x P(odd on second throw) +


P(odd number on first throw) x P(even on second throw)


=


P(X=2) = P(odd number on first throw) x P(odd on second throw)


=


Now we have pi and xi.


Let’s proceed to find mean and variance.


Mean of any probability distribution is given by Mean = ∑xipi


Variance is given by:


Variance = ∑ xi2pi – (∑xipi)2


first we need to find the products i.e. pixi and pixi2 and add them to get mean and apply the above formula to get the variance.


Following table representing probability distribution gives the required products :



Variance = ∑ xi2pi – (∑xipi)2


Variance =


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