Assume that Z, V, and V, are independent ran and V2 ~ x²(9). Find the following: (a) P[V + V < 8.6]. (b) P[Z//V,/5 < 2.015]. (c) P[Z > 0.611/V].

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18. Assume that Z, V, and V, are independent random variables with Z ~
N(0, 1), V ~x(5),
and V ~ x²(9). Find the following:
(a) P[V + V½ < 8.6].
(b) P[Z//V,/5 < 2.015].
(c) P[Z > 0.611/V].
(d) P[V/V, < 1.450].
(e) The value b such that P
< b
+ V2
= 0.90.
Transcribed Image Text:18. Assume that Z, V, and V, are independent random variables with Z ~ N(0, 1), V ~x(5), and V ~ x²(9). Find the following: (a) P[V + V½ < 8.6]. (b) P[Z//V,/5 < 2.015]. (c) P[Z > 0.611/V]. (d) P[V/V, < 1.450]. (e) The value b such that P < b + V2 = 0.90.
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