Let X be a random variable with probability density function given by f(x) = { 2(1 – 2), 0


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Let X be a random variable with probability density function given by<br>f(x) = { 2(1 – 2), 0<I<1<br>0,<br>elsewhere<br>a. Use the method of distribution functions to find the density function of U1<br>2X – 1.<br>b. Use the method of transformations to find the density function of U1 = 2x-1.<br>c. Use the method of distribution functions to find the density function of U2 =<br>1- 2X.<br>d. Use the method of transformations to find the density function of U2 = 1–2X.<br>e. Use the method of distribution functions to find the density function of U3 =<br>X².<br>f. Find E(U3) using the density function got in part e, and compare it with the result<br>using E[U3] = Sr²f(x)dr<br>

Extracted text: Let X be a random variable with probability density function given by f(x) = { 2(1 – 2), 0
Jun 11, 2022
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