A needle is free to swing. It is equally likely to come to rest at any...

 

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A needle is free to swing. It is equally likely to come to rest at any angle between 0 and л. (a) What is the probability density, p(0)? Graph the probability density, p(0), as a function of from π/2 to 3π/2. (b) Compute (0), (02), and σ for this distribution. (c) Compute (sin 0), (cos 0), and (cos²0). A needle is free to swing. It is equally likely to come to rest at any angle between 0 and л. (a) What is the probability density, p(0)? Graph the probability density, p(0), as a function of from π/2 to 3π/2. (b) Compute (0), (02), and σ for this distribution. (c) Compute (sin 0), (cos 0), and (cos²0).