Suppose we are given a random number generator, which emits random numbers drawn according to the...

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Suppose we are given a random number generator, which emits random numbers drawn according to the uniform distribution (0, 1) (like the rand command in MATLAB). Using this device, we are asked to generate a random variable drawn according to a given distribution F(-). (a) If X is a random variable with a distribution F(x), show that Y = F(X) is uniformly distributed, i.e., YU(0, 1). (b) Using the insights you draw from part (a), describe how to achieve the desired task. Show your result. Suppose we are given a random number generator, which emits random numbers drawn according to the uniform distribution (0, 1) (like the rand command in MATLAB). Using this device, we are asked to generate a random variable drawn according to a given distribution F(-). (a) If X is a random variable with a distribution F(x), show that Y = F(X) is uniformly distributed, i.e., YU(0, 1). (b) Using the insights you draw from part (a), describe how to achieve the desired task. Show your result.

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Part a To prove that Y FX is uniformly distributedwe need to show that FX is a monotonically increasing functionThis means that for any two values of Xif X1 X2then FX1 FX2 If FX is monotonically incre... View the full answer