Suppose X1 and X2 have joint density function { fx,,x2 ("1, #2) 0, O.W. E[X1]E[X2] Find the marginal density of X1 and X2. Find E[X1X2], E[X1], and E[X2]. Notice that E[X1X2] = and X1 and X2 are not independent.

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A: For a continuous variable X, the cumulative distribution function Fx can be given as Fx=∫-∞xfxdx,…

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Q: 9

A: 7.42 From the given information, the joint density function for X and Y is,

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Q: Let X and Y have the joint density function 6x y, 0<x<1,0<y<1, (0, f(x.y)= Otherwise.

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Q: Suppose X has density, find EX* f(x) = Lo 2x for 0≤x≤1 otherwise O 1/2 O 3/4 O 2/3 Does not exist

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A: We have given that  To determine relative maximum we differentiate the given pdf and equat to zero.

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A: Given,f(x,y)=34(x2+y2)  ;  -1&lt;x&lt;1 , 0&lt;y&lt;1

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Q: Find c. b. Find the cdf. c. What is P(.1≤ X <.5)

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!