1) Let Y be a r.v which has the pdf as belowf(y)=e-²/0,y>0= 0,0.wUsing jacobian method find the distribution of U=Y2. (It's a one to one function since y is always positive).

Here we have given the probability density function of random variable y We have to find the…

Answered: 1) Let Y be a r.v which has the pdf as…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let X have a pdf of f(x) = 4/15, 3 < X < b. a. What type of distribution does X have? b. Find b such that f(x) is a pdf. c. Find P(3.8 < X < 5.3). Give exact answer(fraction). d. Find μ, σ^2. Give exact answers(fractions).
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3. Let X; N iid U(0, 1) for i e {1, 2, ...,n}. (a) Compute the pdf of Y; = - log(X;), name the distribution that Y; follows and provide any parameter value or values needed. (b) Compute the pdf that W = [I", X, = X1 X2... X, follows. You may use the result given as part of the Example 2.6 video (even though it will only be proved in Chapter 3). (c) Compute E[W] in the two following ways: (i) through exploiting independence of the X, and using EUV] = E[U]E[V] for any independent random variables U and V. (ii) using the pdf of W computed in the previous part.
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Assume that X1, X2, X3 ∼ Exp (λ) are independent and evenly distributed with the distribution Exp (λ = 1). (a) Determine the distribution of Y = X1 + X2 + X3 and state its PDF f (y). (b) Determine the distribution of U = 2Y
The value of the correlation r = (x,y) for the information would be: n = 8, Sum(x) = 609, Sum(y) = 504, Sum (x)^2 = 47995, Sum (y)^2 = 32954, and Sum (xy) = 395650 0.255 0.147 0.855 0.174
Question 2 Let joint pdf for X and Y as follow: f (x, y) = *(2-y) 4 for 0
Which of the following is the correct sum of squared residuals to be minimized to find tne fit f(x) = £ (2r-1)"* - using a data set ((xo, Yo), (x1,y1), --, CKn. Yn)} ? A.) Eo(In(y;) + a – b2x; + 1)² B.) E-(In(y;) + In a + b In(2x; – 1))² D.) E7-o(In(y;) – In a – b In(2x; – 1))² E.) E-o(In(y;) + In a – b2x; + 1)²
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fx₁x (x₁y) = х-у 2e-x-y if x 71 9710 {26-23 2⁰ } otherwise J Find fycy) and fx cx) where fxiy (xiy) is joint pdf and fycy) / fx(x) are marginal distribution functions -
Let W ~ Gamma(100, 3.4). (a) Give the exact value of P(1.5 < W < 5.0) (b) Give the approximate value of P(1.5 < W < 5.0) using normal approximation

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1) Let Y be a r.v which has the pdf as below f(y) (2)e-v²/0,y>0 = 0,0.w Using jacobian method find the distribution of UY2. (It's a one to one function since y is always positive).