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The number of cartoons X, watched by Mrs. Kelly's first grade class on Saturday morning is shown below.


X P(X)

0 0.15

1 0.20

2 0.30

3 0.10

4 0.20

5 0.05

Give the standard deviation for the probability distribution above.

Verified Answer :

syed514

The standard deviation σ is the square root of the variance:σ=V(X)−−−−−√=E(X2)−(E(X)2−−−−−−−−−−−−−√)where E(X)is the expected value of X. By definition,E(X)=∑x∈Dxp(x)where D is the values X may take (in this case D={0,1,2,3,4,5})and p(x)=P(X=x)is the probability that X equals x.Then,E(X)==0⋅p(0)+1⋅p(1)+2⋅p(2)+3⋅p(3)+4⋅p(4)+5⋅p(5)2.15.
Similarly,E(X2)==02⋅p(0)+12⋅p(1)+22⋅p(2)+32⋅p(3)+42⋅p(4)+52⋅p(5)6.75,soV(X)=6.75−2.15=4.6andσ=4.6−−−√≈2.144.

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