8/17/2019 PS_Sol_Ass_4_2015

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Probability and StatisticsHints/Solutions to Assignment No. 4

1. The range of Y is 0 to 4. For 0 ≤ y ≤ 1, there are two inverse images y and

y−

. For 1 < y < 4, there is one inverse image y . Using these we get thedensity of Y as

1/2Y

1/2

2f (y) y , 0 y 1,

91

(1 y ), 1 y 4,90, elsewhere.

−

−

= ≤ ≤

= + < <

=

2. The argument is same as in Problem 1.3. Here also Y is two- to-one function of X in the given domain.

Problem 4 to 8 are straightforward..

9. The density of Y is obtained as

Y

1f (y) , 0 y 1,

23 y

, 1 y 3,4

0, elsewhere.

= ≤ ≤

−= < ≤

=