Let X be uniformly distributed on -1-1-- Find the density of Y-Xk for.docx
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Let X be a uniformly distributed random variable on the interval [1, 1]. To find the density of Y = X^k, where k is a positive integer, differentiate between whether k is odd or even. Use the method from class of finding the density of a transformation of a random variable to determine the density of Y.
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![Let X be uniformly distributed on [ 1 , 1 ] . Find the density of Y = X k for positive integers k .
Hint : differentiate the cases k odd/even and use the same method as we did in class for the case
X 2 where X was a normal random variable, using the formula for the density of a tranformation
of a random variable](https://image.slidesharecdn.com/letxbeuniformlydistributedon-1-1-findthedensityofy-xkfor-230223044906-ac29197c/85/Let-X-be-uniformly-distributed-on-1-1-Find-the-density-of-Y-Xk-for-docx-1-320.jpg)
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public void setIndex(int i) {
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}
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return index;
}
public void setIndex(int i) {
index = i;
}
}
public static final int CAPACITY = 16;
private ArrPos<E>[] data;
private int size = 0;
public ArrayPositionalList() {
this(CAPACITY);
}
public ArrayPositionalList(int capacity) {
data = (ArrPos<E>[]) new ArrPos[capacity];
}
@Override
public int size() {
return size;
}
@Override
public boolean isEmpty() {
return size == 0;
}
@Override
public Position first() {
if (!isEmpty())
return data[0];
return null;
}
@Override
public Position last() {
if (!isEmpty())
return data[size - 1];
return null;
}
@Override
public Position before(Position p) throws IllegalArgumentException {
if (p.getIndex() > 0 && p.getIndex() < size) {
return data[p.getIndex() - 1];
}
if (p.getIndex() == 0)
return null;
throw new IllegalArgumentException();
}
@Override
public Position after(Position p) throws IllegalArgumentException {
if (p.getIndex() >= 0 && p.getIndex() < size - 1) {
return data[p.getIndex() + 1];
}
if (p.getIndex() == size - 1)
return null;
throw new IllegalArgumentException();
}
@Override
public Position addFirst(E e) {
if (size < data.length) {
for (int i = size - 1; i >= 0; i--) {
data[i + 1] = data[i];
data[i + 1].setIndex(data[i + 1].getIndex() + 1);
}
data[0] = new ArrPos<E>(e, 0);
size++;
return data[0];
}
return null;
}
@Override
public Position addLast(E e) {
if (size < data.length) {
da.
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