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Let X, Y, and Z be jointly continuous random variables. Assume that all conditional PDFS and expectations are well defined. E.g.
1 answer:
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Answer:
The set of polynomial is linearly independent
Explanations:
For clarity and easiness of expression, the complete solution is handwritten in the file attached. However, the following are the steps taken:
1) The coordinate vectors of the polynomials are formed as:
(1,0,6,-1), (0,1,02) and (1,1,6,0)
2) A matrix is formed using the coordinates of the polynomials as the columns of the matrix
3) The polynomial formed is row reduced to form an echelon matrix.
4) As seen from the reduced echelon form of the matrix, the rank of the matrix = 3
5) since the rank = number of polynomials = 3, the set of polynomials is linearly independent.
Given functions are:
and
Using both functions we need to find value of (f*g)(x)
(f*g)(x) simply means find product of f(x) and g(x) so we will multiply values of each function as shown below:
Hence final answer is .