Get inspired by the success stories of our students in IIT JAM MS, ISI  MStat, CMI MSc DS.  Learn More

# Probability Theory | ISI MStat 2015 PSB Problem B5 This is a detailed solution based on Probability Theory of ISI MStat 2015 PSB Problem B5, with the prerequisites mentioned explicitly. Stay tuned for more.

## Problem

Suppose that and are random variables such that Var Var (a) Evaluate Cov .
(b) Show that .
(c) If in addition, it is given that is bivariate normal, calculate E .

### Prerequisites

• Basic Probability theory ( Expectation, Variance, and Covariance )
• Normal Distribution
• Gamma Integral

## Solution

(a) Using , we use Var - Var =  .

(b)

Say  . .

Do you remember the Cauchy - Schwartz Inequality? . Hence, .

(c) and . is bivariate normal ~ .   .

This is a detailed solution based on Probability Theory of ISI MStat 2015 PSB Problem B5, with the prerequisites mentioned explicitly. Stay tuned for more.

## Problem

Suppose that and are random variables such that Var Var (a) Evaluate Cov .
(b) Show that .
(c) If in addition, it is given that is bivariate normal, calculate E .

### Prerequisites

• Basic Probability theory ( Expectation, Variance, and Covariance )
• Normal Distribution
• Gamma Integral

## Solution

(a) Using , we use Var - Var =  .

(b)

Say  . .

Do you remember the Cauchy - Schwartz Inequality? . Hence, .

(c) and . is bivariate normal ~ .   .

This site uses Akismet to reduce spam. Learn how your comment data is processed.

### Knowledge Partner  