Question:

1. In either Vanilla JavaScript or in the React framewok, a TODapplication that meets the following requirements:

a. Show an unordered list of todo descriptions that starts as an empty list.

b. Provide a button that when clicked will allow you to type in a todo description and it will show as a list item in the unordered list. (You can use a Javascript prompt.)

c. checkbox next to each todo description in the unordered list.

d. Make a label and value that keeps track of the count of list items.

e. Make a label and value that keeps track of the count of list items that are not checked.

2. As a challenge - not required - try adding the ability to delete each list item by adding a DELETE button to each list item that removes the item when it is clicked.

X and Y are jointly Gaussian random variables. Which one of the following statements is not necessarily true? 0 X + Y and X + 2Y are also two jointly Gaussian random variables. 0 X + Y and X - Y are also two jointly Gaussian random variables. 0 5+2X+Y has a Gaussian distribution 0 X + Y and X Y are independent. 0 X and Y are uncorrelated if and only ifthey are independent. 0 X + Y is a Gaussian random variable. . This homework is designed to make you familiar with different random variable generating functions in MATLAB. Problem 1: Gaussian Random Variable (a) Generate a Gaussian random variable with mean = 0, variance = 1. (b) Generate a Gaussian random variable with mean = 5, variance = 0.1. (c) Generate a 10-by-1 sequence of Gaussian random variables whose each element is independent and identically distributed with mean = 0, variance = 1. (d) Repeat the problems (a) to (c) when the Gaussian random variables have ex- pected value = 5 and variance = 0.01.(a) Let X and Y be jointly Gaussian random variables with means ux and My and standard deviations ox and oy respectively, and correlation coefficient pxy. Define new random variables Uj and U2 by the transformation. U1 = ( X - ux) / ox + ( Y - MY) /Ox U2 = ( X - ux) /OX - (Y - MY) /OY Show that U1 and U2 are Gaussian random variables with zero means and zero correlation coefficient. How would you modify the transformation to obtain two new independent Gaussian random variables Vi and V2 with zero means and unit variances? Note: The above illustrates how you can transform two correlated Gaussian random variables X and Y to two uncorrelated and independent standard normal Gaussian random variables Vi and V2