Let X be a uniformly distributed continuous random variable that can take values in the interval (-1,1). Y Let Y=1-X2 be defined as a function of the random variable X. a) Mathematically find the probability density function (PDF) of Y. b) Find mathematically the covariance, Cov[X,Y], of X and Y. X and Y are uncorrelated (uncorrelated)? Are X and Y independent? c) With the help of the "rand" command in MATLAB, the random variable X is randomized into 1,000,000 random variables. and the corresponding Y=1-X2 values. Plot the histogram of Y. The histogram you found in (a) Does it match the PDF? Comment. d) Estimate Cov[X,Y] using the 1,000,000 X and Y values you generated in MATLAB obtain For this, from the definition Cov[X,Y] = E[(X-E[X])(Y-E[Y])] and the "mean" command Does it match the value you found in (b)? Comment.
Let X be a uniformly distributed continuous random variable that can take values in the interval (-1,1). Y
Let Y=1-X2 be defined as a
a) Mathematically find the probability density function (
b) Find mathematically the
(uncorrelated)? Are X and Y independent?
c) With the help of the "rand" command in MATLAB, the random variable X is randomized into 1,000,000 random variables.
and the corresponding Y=1-X2 values. Plot the histogram of Y. The histogram you found in (a)
Does it match the PDF? Comment.
d) Estimate Cov[X,Y] using the 1,000,000 X and Y values you generated in MATLAB
obtain For this, from the definition Cov[X,Y] = E[(X-E[X])(Y-E[Y])] and the "mean" command
Does it match the value you found in (b)? Comment.
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