contestada

x 13 16 18 21 23 25 26 31
p(x) .07 .21 .17 .25 .05 .04 .13 .08
the mean of the discrete random value variable x is the 20.59. What is the variance of X?
Round your answer to the nearest hundredth
a 27.89
b27.89
c33.15
d23.18

Respuesta :

LammettHash
First compute the second moment:

[tex]\mathbb E[X^2]=\displaystyle\sum_x x^2p(x)=13^2\cdot0.07+\cdots+31^2\cdot0.08\approx447.13[/tex]

Then the variance of [tex]X[/tex] is

[tex]\mathbb V[X]=\mathbb E[X^2]-\mathbb E[X]^2\approx447.13-20.59^2\approx23.18[/tex]

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