- #1

gajohnson

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## Homework Statement

Let

f(x) = (1 + cx)/2 for x between -1 and 1 and f(x)=0 otherwise, where c is between -1 and 1. Show that f is a density and find the corresponding cdf. Find the quartiles and the median of the distribution in terms c.

## Homework Equations

NA

## The Attempt at a Solution

I simply showed that this was a density by integrating f(x) from -1 to 1 and showing that this is 1.

For the second part of the problem, I found the CDF to be F(x) = 1/2(x+(cx^2)/2) for -1≤x≤1.

Clearly, F(x) = 0 for -1<x. However, is F(x) = 1 for x>1?

In addition, I am having trouble properly interpreting the directions for finding the quartiles and median. Should my answer be a function of c? If so, how do I go about getting there? Thank you!

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