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MAT 221 Lecture Notes - Lecture 9: Random Variable

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School
Syracuse University
Department
Mathematics
Course
MAT 221
Professor
Au

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MAT 221 Full Course Notes
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MAT 221 Full Course Notes
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If x and y are two random variables, then. If x is a random variable and a and b are fixed numbers, then. Example 1: consider the following random variable x: The mean of x is x = (2)(0. 4) + (3)(0. 6) = 2. 6. Example 3: linda is a sales associate at an auto dealership. For a saturday, she estimates her sales as follows: (chart on slides) The mean of s is s = (0)(0. 3) + (1)(0. 4) + (2)(0. 2) + (3)(0. 1) = 1. 1. The mean of t is t = (0)(0. 4) + (1)(0. 5) + (2)(0. 1) = 0. 7.

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PROBLEM 17: A random variable X takes four possible values, 0, 2, a, and b, where a and bare unknown numbers. If Pr[x = 0) = 0.2, Pr[X=2] = 0.4, Pr[X = a) = 0.3, E[X] = 2.8 and it is the case that a + b = 6, what is the missing value of a ? A) -1.0 B) 5.0 C) 7.0 D) cannot be determined without more information E) none of the above

3) Find the derivatives of the following functions and simplify your answers (they should be pretty simple).

a) y=18arcsin(x/6) + x/2sqrt(36-x^2) +24 (show your work)

b). y=xarctan(3x)-1/6ln(9x^2 +1) + 1 (show your work).

c). y=be^(ax)sin(bx)+ae^(ax)cos(bx) (where a and b are constants. show your work)