Recent content by alpines4

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    Showing X Vector Concentrated Around Unit Sphere Convergence of Mean-Squared

    Homework Statement Let Y_i be standard normal random variables, and let X be an N vector of random variables, X=(X_1, ..., X_N) where X_i = 1/{sqrt{N}} * Y_i. I want to show that as N goes to infinity, the vector X becomes "close" to the unit sphere. Homework Equations The...
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    How Do You Derive the PDF of a Linearly Transformed Vector?

    Homework Statement Define X to be an n-vector of jointly continuous random variables X1, ..., Xn with joint pdf f(x) mapping R^n to R. Let A be an invertible nxn matrix and set Y=AX+b. I want to derive the pdf of f(y) in terms of f(x), the original pdf. Homework Equations The...
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    Penny flipped and uniform PDF generated

    Thank you for your help, Ray.
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    Penny flipped and uniform PDF generated

    Homework Statement A penny is flipped until we see the first head, and flips are assumed to be independent. For each tail we observe before the first head, the value of a continuous random variable with uniform PDF over the interval [0,3] is generated. Let the RV X be the sum of all the...