Remeber that it is areas under a density curve, not the height of the curve, that give proportions in a distribuiton. To illustrate this, sketch a density curve that has its peak at 0 on the horizontal axis but ahs greater area within .25 on either side of 1 than within .25 on either side of 0
I have no idea how to do this...
To create a density curve that satisfies the given conditions, we can follow these steps:
1. Start by drawing a horizontal axis, representing the value range of the variable.
2. Identify the peak of the density curve located at 0 on the horizontal axis. Plot this point on the graph.
3. Now, consider the area within 0.25 on either side of 1. This area needs to be greater than the area within 0.25 on either side of 0. To achieve this, we need to make the density curve greater or higher in the range around 1 than around 0.
4. You can make the density curve greater by increasing the height of the curve in the range from 0.75 to 1.25. This will create a peak around 1 and increase the area within 0.25 on either side of 1. Similarly, make the density curve lower in the range from -0.25 to 0.25 to decrease the area within 0.25 on either side of 0.
5. Connect the points you have plotted smoothly to construct the curve. Remember, a density curve should be continuous and non-negative.
By following these steps, you should be able to sketch a density curve that satisfies the given conditions. Remember that the curve's height does not necessarily represent the proportion; it's the area under the curve that gives proportions in a distribution.