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# Discover the Covariance | ISI MStat 2016 Problem 6 This problem from ISI MStat 2016 is an application of the ideas of indicator and independent variables and covariance of two summative random variables.

## Problem- Covariance Problem

Let ~ be i.i.d. random variables from a continuous distribution whose density is symmetric around 0. Suppose . Define .
Calculate the covariance between and .

This problem is from ISI MStat 2016 (Problem #6)

### Prerequisites

1. X has Symmetric Distribution around 0 .
2. , where is a random variable.
3. and are independent  and are independent.
4. and are independent .

## Solution  .

Let's calculate the covariance of and .   .

This problem from ISI MStat 2016 is an application of the ideas of indicator and independent variables and covariance of two summative random variables.

## Problem- Covariance Problem

Let ~ be i.i.d. random variables from a continuous distribution whose density is symmetric around 0. Suppose . Define .
Calculate the covariance between and .

This problem is from ISI MStat 2016 (Problem #6)

### Prerequisites

1. X has Symmetric Distribution around 0 .
2. , where is a random variable.
3. and are independent  and are independent.
4. and are independent .

## Solution  .

Let's calculate the covariance of and .   .

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