f(x)=kx2e−x,x>0
i) ∫f(x)dx=1
∫0∞kx2e−xdx=k∫0∞x2e−xdx=/integrating by parts/=2k=1
k=1/2
ii) mean
M[x]=∫0∞xf(x)dx=k∫0∞x3e−xdx=/integrating by parts/=6k=3
M[x]=3
iii) variance
D[x]=M[x2]−(M[x])2
M[x2]=∫0∞x2f(x)dx=k∫0∞x4e−xdx=/integrating by parts/=24k=12
D[x]=12−(3)2=12−9=3
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