et X1, X2, X3, X4 have the joint probability density function f(x1, x2, x3, x4) = ( 24e −(x1+x2+x3+x4) , 0 < x1, x2, x3, x4 < ∞ 0, elsewhere Let Y1 = X1, Y2 = X2 − X1, Y3 = X3 − X2, Y4 = X4 − X3. (i) Using the change of variable technique, find the joint probability density function of Y1, Y2, Y3, Y4
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Let X1, X2, X3, X4 have the joint probability density function
f(x1, x2, x3, x4) = (
24e
−(x1+x2+x3+x4)
, 0 < x1, x2, x3, x4 < ∞
0, elsewhere
Let Y1 = X1, Y2 = X2 − X1, Y3 = X3 − X2, Y4 = X4 − X3.
(i) Using the change of variable technique, find the joint probability density function
of Y1, Y2, Y3, Y4
(ii) Find the conditional distribution of Y4 given Y1, Y2, Y3
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