Random Variables

3 cards are drawn in succession from a regular straight deck of 52 playing cards. Find the probability that: (a) the first card is a Red Ace. (b) the second card is a 10 or Jack. (c) the third card is greater than 3 but less than 7.

12.5-2

We are using the book Methods of Real Analysis by Richard R. Goldberg (See attached file for full problem description) --- 12.5-2 Show that the Fourier series for is a) Use 12.5E to show that Fourier series at t=0 converges to . Deduce that 12.5E: Theorem. Let ( this means the function f and the function g is Lebesgue Integrable on , we can write , pag 318 of the book Methods if real analysis by Richard R. Goldberg), and let x be any point in . If and exist, then the Fourier series for at x will converge to . b) Use Parseval's equality to show that ... click for more

12.6-3

We are using the book Methods of Real Analysis by Richard R. Goldberg (See attached file for full problem description) --- 12.6-3 Let be a complete orthogonal family in . Define the function A from into .( This means: In order to manufacture our metric space we must therefore regard any two function whose values are equal almost everywhere as representing the same point in our space. This is,the points in the space-which we denote by -are, by definition, classes of square integrable functions, the functions in any one class differing from one another only on sets of measure zero. ---

12.6-1

(See attached file for full problem description) --- 12.6-1 Calculate the Legendre functions and show that they are orthogonal to one another on [-1,1] and that each has norm equal to 1.

Showing a quotient space is a complete metric space

Let (X,B,mu) be a complete, finite measuable space. For each C,D in B, set d(C,D) = mu (C / D) where C / D is the symmetric difference of C and D. We say that two measurable sets C,D are equivalent if d(C,D)=0 (this is an equivalence relation). Let E be the set of equivalence classes, and show that d introduces a metric on E and that (E,d) is a complete metric space.