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What is the value of b

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Reference no: EM13828478

1. What do the following stand for?

65_notation.png

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 ) + ......... (xk2 + yk2 )

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

nΣk=1 k = n(n+1)/2

Use the preceding formula to evaluate

2049_notation1.png

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

nΣk=1 k2 = n(n+1)(2n+1)/6

Using this formula, obtain

48_notation2.png

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).

Reference no: EM13828478

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