2. Assume that the pdf of the random variable x is uniform in the interval (10, 12) and y = x^3.
(a) Find fy (y).
(b) Find E{y}.
a)
here CDF of Y: F(y)=P(Y<y)=P(X3 <y)=P(X<y1/3)=(f(x) dx=(1/2) dx=(x/2)|y1/310 =(1/2)*(y1/3-101/3)
therefore pdf f(y)=(d/dy)*F(y)=(1/6)*y-2/3 for 1000<y<1728
b)
E(Y)=E(X3)= x3(f(x) dx =x3/2 dx =x4/8 |1210 =1342
2. Assume that the pdf of the random variable x is uniform in the interval (10,...
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