r***a
发帖数: 58 | 1
area = X*Y
E(area) = E(X*Y)= E(E(Y|X)X)=E(X/2*X) = 1/6
do mathematics yourself. :) | J**Y
发帖数: 34 | 2 X is an exponential r.v., so it's density function is: f(x)=t*exp(-t*x), if
x>=0 and f(x)=0 if x<0, t>0.
Because it's std=d, we can know d=1/t => t=1/d. We can also know that
E(X)=1/t=d. So, P(|X-E(X)|>kd)=P(|X-d|>kd)=P[(X-d)<-kd]+P[(x-d)>kd]
=P[Xd(1+k)]. According to your values of k, d(1-k)<0 =>
P[X
P[X>d(1+k)]=1-Integrate[(1/d)*Exp[-x/d], {x,0,d(1+k)}]
=Exp[-k-1] | J**Y
发帖数: 34 | 3 The expected circumstance is E(2*X+2*Y)=2*E(X+Y)=
2E(X)*Integrate[p(y|x), {y,0,x}]+2*Integrate[p(x)*E(Y|X), {x,0,1}]
=2E(X)+E(X)=3/2 |
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