A question on continuous random variable Let say, I have 2 continuous random variables X1 & X2. Both have same location parameters. Other parameters may be same or may not.
Now say, the q1-th quantile of X1 is less than the q1-th quantile of x2. But the q2-th quantile of x1 is more than the q2th quantile of x2.
My question is, is that possible? Is there any example of x1 & x2 which have that property?
I will be really grateful if someone can give me some pointer.

Edit: At this point, I realize the question I asked for was not correctly specified. 
I'm particularly interested in the case where the two quantiles being considered are on the same side of the location parameter. 
 A: Since you appear to doubt the example offered, I have included a diagram. As Michael Mayer said, two normal distributions centered around 0, one with larger variance, is sufficient.
In the diagram, we compare the 0.1 and the 0.9 quantiles for $\sigma=1$ (blue) and $\sigma=0.8$ (dark orange)

Michael Mayer's example fulfills the requirements of your question with $q_1=0.1$, $q_2=0.9$ and $X_1$ being the one with larger variance.

Edit:
For the case where $q_1$ and $q_2$ must both be on the same side of whatever the measure of location is, let's take two symmetric distributions, which share the same mean and median.
Let $X_1$ be $\sim \text{N}(0,1^2)$ and let $X_2$ be an equal mixture of a $\text{N}(-0.8,0.1^2)$ and a  $\text{N}(0.8,0.1^2)$, and let $q_1 = 0.6$ and $q_2 = 0.9$:

This example fulfills the new requirements of your question with $q_1=0.6$, $q_2=0.9$ and $X_1$ being the one with only a single normal component (shown in blue above).
Further, you should note that 'location parameter' isn't sufficiently specified. I could parameterize normal distributions by their 5th percentile and their standard deviation, and call the parameter based on the 5th percentile the location parameter (it's just a shift of the mean by $1.645\sigma$. and can work as a perfectly valid location parameter). Then Michael's original example suffices even under the new conditions. If that contradicts your intention, your intention needs to be stated specifically enough to exclude it.
