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If x and y are two independent random variables then their joint density function is given by
The density function fz of the sum of these two variables is given by the convolution
The proof of this relation may be found in any good introductory text on probability. According to the preceding exercise, if x and y are each U[0,1] then their joint density is triangular, i.e., t = rlr, using symbol t for triangle. What has the central limit theorem got to do with this process of repeated convolution?
If x and y are two independent random variables then their joint density function is given by The density function f z of the sum of these two variables is given by the c
Question 1 Find all solutions of the following equations in the interval [0, 2π) (a) sin(2x) = √2 cos(x). (b) 2 cos 2 (x) + 3 sin(x) = 3. 2. Sketch the graph of the ci
A manager has determined the cost C, in dollars, for manufacturing is C(q) =85log 10 (10+q/2) for manufacturing, where q is the number of units produced in a given day. (a
1. (i) How many digits does the number 101000 have when written to base 7 ? (ii) Use the prime number theorem to estimate the proportion of prime numbers among the positive inte
This is a pen and paper exercise, you are expected to provide a detailed derivation. Follow the procedure outlined in the lectures for construction of a simple averaging by thr
In an article in Marketing Science , Silk and Berndt investigate the output of advertising agencies. They describe ad agency output by finding the shares of dollar billing volume
A high school counselor needs to specify whether the teenage pregnancy rate at her school is disimilar from the rate nationwide. She knows that the rate nationwide is 15 %. She ran
how to model equations to determine the amount of oil in a reservior
trigonometric functions
Compute the (real and imaginary parts of the) principal value of the eighth root of (a + ib) to 3 decimal places (accurate to 10 -3 ). Call the real part "m 7 ", and the imagina
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