# Question

A random variable has a CDF given by

(a) Find the mean of X;

(b) Find the variance of X;

(c) Find the coefficient of skewness of X;

(d) Find the coefficient of kurtosis of X.

(a) Find the mean of X;

(b) Find the variance of X;

(c) Find the coefficient of skewness of X;

(d) Find the coefficient of kurtosis of X.

## Answer to relevant Questions

Find the variance and coefficient of skewness for a geometric random variable whose PMF is You may want to use the results of Exercise 4.13. A uniform random variable has a PDF given by fX (x) = u(x) – u (x – 1). (a) Find the mean and variance of X. (b) Find the conditional mean and the conditional variance given that 1 / 2 < X < 3 / 4. Consider a Gaussian random variable, X , with mean µ and variance σ2. The random variable is transformed by the device whose input– output relationship is shown in the accompanying figure. Find and sketch the PDF of the ...Recall the joint CDF given, (a) Find Pr (X < 3/4). (b) Find Pr(X > 1/2). (c) Find Pr (Y > 1/4). (d) Find Pr (1 / 4 < X 1 /2, 1/2 < Y < 1). Consider again the random variables of exercise 5.12 that are uniformly distributed over an ellipse. (a) Find the conditional PDFs, fX|Y (x| y) and fY|X (y|x). (b) Find f X|Y > 1(x). (c) Find fY |{|X| < 1}.Post your question

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