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m_̓mzɂċĂ͂킩Ă̂Ť@Let X be a random variable defined as follows:
X is a real valued function on a sample space W ={(x,y): 0<=x<=1 & 0<=y<=1}, where a probability is given by width, and X satisfies
X((x,y))=8x for all (x,y) in W.
Input the variance V(X), down to two places of decimals
F5.33 ł

: moonhappy
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ŐV̉񓚂

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W{W=$\{(x,y)|0\le~x\le~1,0\le~y\le~1\}$Ťm͍LɂČ܂ƂĂ̂Ťz֐F(x,y)=xymx֐f(x,y)=$F_xy$(KΔ)=1

Ȃ̂Ťl֐X(x,y)=8xɂĂ̊Ғl

$E[X]=\int^{1}_{0}\int^{1}_{0}Xf(x,y)dxdy=\int^{1}_{0}\int^{1}_{0}8xdxdy=4$

$E[X^2]=\int^{1}_{0}\int^{1}_{0}X^2f(x,y)dxdy=\int^{1}_{0}\int^{1}_{0}64x^2dxdy=64/3$

mϐƂĂX̕U

$V[X]=E[X^2]-E[X]^2=64/3-4^2=5.33...$

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