Express the following in thenbspsigma notation and what is

Question

1. What do the following stand for?

2. Express the following in the Σ notation:

a. x₁ + x₂ + x₃ + x₄ + x₅
b. x₁ + 2x₂ + 3x₃ + 4x₄ + 5x₅
c. (x₁² + y₁² ) + (x₂² + y₂² ) + ......... (x_k² + y_k² )

3. It can be shown that the sum of the first n positive numbers is:

ⁿΣ_k=1 k = n(n+1)/2

Use the preceding formula to evaluate

4. It can be proved that the sum of squares of the first n positive numbers is:

ⁿΣ_k=1 k² = n(n+1)(2n+1)/6

Using this formula, obtain

A.12. An r.v. X has the following PDF:

x	f(x)
0	b
1	2b
2	3b
3	4b
4	5b

a. What is the value of b? Why?

b. Find the P( X ≤ 2 ); prob( X ≤ 3 ); prob( 2 ≤ x ≤ 3).