If X and Y are independent random variables with common density f (x) = = for 0 < æ < 2 then (fx * fy) (3)
Q: Suppose that X and Y have a joint probability density function given by ce-3z-5y fxy(x, y) = if x, y…
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A: Introduction: For the exponentially distributed random variables X and Y, with respective parameters…
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A: Answer: For the given data,
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Q: 1) Suppose, the continuous random variable X has density given by fx(x) 4.x*; 0 < x < 1, 0;…
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Q: Suppose that X and Y are random variables with joint density function fx,y (x, y) = 8xy for 0 ÷|Y =…
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A: Solution
Q: Suppose that X and Y have a joint probability density function given by ce-3z-5y fxy(x, y) = if x, y…
A: Given f(x,y)=ce-3x-5y x,y≥0
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A: Considering that total probability is unity ∫-∞∞f(x) dx = 1∫-∞0f(x) dx+∫1∞f(x) dx =10+∫1∞f(x) dx = 1
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A: We use the realtion of cdf and pdf to solve the qstn.
Q: The life lengths of two transistors in an electronic circuit is a random vector (X; Y) where X is…
A: Probability=0.3935 (b)
Q: The life lengths of two transistors in an electronic circuit is a random vector (X; Y ) where X is…
A: Solution
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Q: Suppose that the random variable X has density function fx (x) = bx-1 for 0 < x < 1, where b is a…
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Q: Suppose X and Y are independent random variables. X is uniformly distributed on (0, ) and Y is…
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Q: Suppose that X is a normal random variable with parameters u = 5 and o = 1. Define Y = X2 – 10X +…
A: 1] X is a normal random variable 2] μ=5 and σ=1 3] Y=X2-10X+25
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- If the probability density of X is given by f(x) =2x−3 for x > 10 elsewherecheck whether its mean and its variance exist.Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.Let Xand Y be two continuous random variables with joint probability density [3x function given by: f(x.y)%D 0sysxsl elsewhere with E(X) = ECX)- EC) - EC*)= ;and E(XY) = 10 3 E(Y*) = - and E(XY) =; %3D Then the value of the variance of 2X+Y is: O 3/80 O 91/320 43/320 7/20
- Suppose that two continuous random variables X and Y have joint probability density function fxy = 1sxs2,0sy<3 elsewhere Find the strength of the relationship and interpret the findings.Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; isSuppose that the random variables X, Y, Z have multivariate PDFfXYZ(x, y, z) = (x + y)e−z for 0 < x < 1, 0 < y < 1, and z > 0. Find (a) fXY(x, y), (b) fYZ(y, z), (c) fZ(z)
- 2. Let X be a random variable with density function ) = √(2x² - + f(x) = Find the expected value of g(x) = 2X+1. 8x2 +5x + 6), 1 < x < 2, 0, elsewhereFor the continuous probability function f(x) = Kx² ex when x ≥ 0 find i) k ii) mean iii) variance =(A=X) qIf X is a continuous random variable find the CDF and density of the function y = x/3
- The random vector x obtained by adding the vectors x1, x2 and x3 end-to-end has a multivariate Gaussian distribution. How do you find the distribution of x2?Let X and Y be two continuous random variables having joint pdffX,Y (x, y) = (1 + XY)/4, −1 ≤x ≤1, −1 ≤y ≤1.Show that X ^2 and Y ^2 are independent.Find the variance of the random variable Y where 3 )2,0y < 2 fr(u) 8