Answer :

(i) Given :



To find : mean (π“Š), variance (Οƒ2) and standard deviation (Οƒ)


Formula used :



Mean = E(X) =


Variance = E(X2) -


Standard deviation =


Mean = E(X) = = x1P(x1) + x2P(x2) + x3P(x3) + x4P(x4)


Mean = E(X) = 0() + 1() +2() +3() = 0 + + + = = =


Mean = E(X) = = 1.2


= = 1.44


E(X2) = = P(x1) + P(x2) + P(x3) + P(x4)


E(X2) = () + () + () + () = 0 + + + = =


E(X2) = 2


Variance = E(X2) - = 2 – 1.44 = 0.56


Variance = E(X2) - = 0.56


Standard deviation = = = 0.74


Mean = 1.2


Variance = 0.56


Standard deviation = 0.74


(ii) Given :



To find : mean (π“Š), variance (Οƒ2) and standard deviation (Οƒ)


Formula used :



Mean = E(X) =


Variance = E(X2) -


Standard deviation =


Mean = E(X) = = x1P(x1) + x2P(x2) + x3P(x3) + x4P(x4)


Mean = E(X) = 1(0.4) + 2(0.3) +3(0.2) +4(0.1) = 0.4 + 0.6 + 0.6 + 0.4 = 2


Mean = E(X) = 2


= = 4


E(X2) = = P(x1) + P(x2) + P(x3) + P(x4)


E(X2) = (0.4) + (0.3) + (0.2) + (0.1) = 0.4 + 1.2 + 1.8 + 1.6 = 5


E(X2) = 5


Variance = E(X2) - = 5 – 4 = 1


Variance = E(X2) - = 1


Standard deviation = = = 1


Mean = 2


Variance = 1


Standard deviation = 1


(iii) Given :



To find : mean (π“Š), variance (Οƒ2) and standard deviation (Οƒ)


Formula used :



Mean = E(X) =


Variance = E(X2) -


Standard deviation =


Mean = E(X) = = x1P(x1) + x2P(x2) + x3P(x3) + x4P(x4)


Mean = E(X) = -3(0.2) + (-1)(0.4) + 0(0.3) + 2(0.1)= -0.6 - 0.4 + 0 + 0.2 = -0.8


Mean = E(X) = -0.8


= = 0.64


E(X2) = = P(x1) + P(x2) + P(x3) + P(x4)


E(X2)= (0.2) + (0.4) + (0.3) + (0.1) = 1.8 + 0.4 + 0+ 0.4 = 2.6


E(X2) = 2.6


Variance = E(X2) - = 2.6 – 0.64 = 1.96


Variance = E(X2) - = 1.96


Standard deviation = = = 1.4


Mean = -0.8


Variance = 1.96


Standard deviation = 1.4


(iv) Given :



To find : mean (π“Š), variance (Οƒ2) and standard deviation (Οƒ)


Formula used :



Mean = E(X) =


Variance = E(X2) -


Standard deviation =


Mean = E(X) = = x1P(x1) + x2P(x2) + x3P(x3) + x4P(x4) + x5P(x5)


Mean = E(X) = -2(0.1) + (-1)(0.2) + 0(0.4) + 1(0.2) + 2(0.1)


Mean = E(X) = -0.2 - 0.2 + 0 + 0.2 + 0.2 = 0


Mean = E(X) = 0


= = 0


E(X2) = = P(x1) + P(x2) + P(x3) + P(x4) + P(x5)


E(X2) = (0.1) + (0.2) + (0.4) + (0.2) + (0.1)


E(X2) = 0.4 + 0.2 + 0 + 0.2 +0.4 = 1.2


E(X2) = 1.2


Variance = E(X2) - = 1.2 – 0 = 1.2


Variance = E(X2) - = 1.2


Standard deviation = = = 1.095


Mean = 0


Variance = 1.2


Standard deviation = 1.095


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