1. Let X be a random variable with probability function f(r) = c(r + 1)² for z = 0, 1.2.3. Find the constant c so that f(r) is a valid probability function, and then derive the mean of X. 2. Pascal's triangle gives a method for calculating the binomial coefficients. It begins as follows: 1 1 1 5 1 4 1 3 10 1 2 6 1 3 10 1 5 8 The (n+1)th row of this table gives the coefficients for (a+b)* = Σra (") a² The next row is found by adding the two numbers above the new entry, i.e. (-)-(-))+ (7) (r= 1,...n-1) Prove this equation using the mathematical definition of a combination.
1. Let X be a random variable with probability function f(r) = c(r + 1)² for z = 0, 1.2.3. Find the constant c so that f(r) is a valid probability function, and then derive the mean of X. 2. Pascal's triangle gives a method for calculating the binomial coefficients. It begins as follows: 1 1 1 5 1 4 1 3 10 1 2 6 1 3 10 1 5 8 The (n+1)th row of this table gives the coefficients for (a+b)* = Σra (") a² The next row is found by adding the two numbers above the new entry, i.e. (-)-(-))+ (7) (r= 1,...n-1) Prove this equation using the mathematical definition of a combination.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:AMERAL Assignment component of your final mark.
1. Let X be a random variable with probability function f(x) = c(r + 1)² for z =
0.1.2.3. Find the constant c so that f(r) is a valid probability function, and then
derive the mean of X.
INAIN
2. Pascal's triangle gives a method for calculating the binomial coefficients. It begins
as follows:
1
5
4
3
10
2
6
I
3
10
1
4
5
1
1
The (n+1)th row of this table gives the coefficients for (a+b)" = Σra (") a
The next row is found by adding the two numbers above the new entry, i.e.
(r= 1,...n-1)
(-)-(-))+(^7)
Prove this equation using the mathematical definition of a combination.
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