Homework Answers
Thegiven PDF is 
1) The condition for PDF is
![4 f(x)dx 1 1 4 k(-x25x- 4)dx 1 k-x3/35x2/2-4x] 1 1 2 2 k OINN/o](http://img.homeworklib.com/questions/58a5f440-7ba4-11eb-abc5-f5225433814f.png?x-oss-process=image/resize,w_560)
2) The expected value is
3) The mode 
is such that
4) The CDF is
![Fx(x) f(t)dt 1 k(-t2 5t 4)dt Fx(x) = Fx(x) k(-t3/35t2/2 4t] x3 1 5(x2- 1) 4(x-1)) Fx(x) k 3 2 5x2 4Xt x3 2 11 ;1 x 4 6 Fx(x)](http://img.homeworklib.com/questions/75e4fa10-7ba4-11eb-9dd6-81c17967562b.png?x-oss-process=image/resize,w_560)
5) The probability,
6) The median is such that 
.
From part (5), we see that 
The shape of the distribution is an inverted parabola, symmetric
about the lin 
.
Thegiven PDF is 
1) The condition for PDF is
![4 f(x)dx 1 1 4 k(-x25x- 4)dx 1 k-x3/35x2/2-4x] 1 1 2 2 k OINN/o](http://img.homeworklib.com/questions/7d92d590-7ba4-11eb-a983-d9816e8c768d.png?x-oss-process=image/resize,w_560)
2) The expected value is
3) The mode 
is such that
4) The CDF is
![Fx(x) f(t)dt 1 k(-t2 5t 4)dt Fx(x) = Fx(x) k(-t3/35t2/2 4t] x3 1 5(x2- 1) 4(x-1)) Fx(x) k 3 2 5x2 4Xt x3 2 11 ;1 x 4 6 Fx(x)](http://img.homeworklib.com/questions/90eebd30-7ba4-11eb-bce2-3de004da598e.png?x-oss-process=image/resize,w_560)
5) The probability,
6) The median is such that 
.
From part (5), we see that 
The shape of the distribution is an inverted parabola, symmetric
about the lin 
.
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