2. A continuous random variable X has probability density function f(x) = c(1+x)(1 – xº) over the domain -1

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2 A Continuous Random Variable X Has Probability Density Function F X C 1 X 1 Xo Over The Domain 1 X 1 A I 1 (56.38 KiB) Viewed 63 times

2. A continuous random variable X has probability density function f(x) = c(1+x)(1 – xº) over the domain -1<x< 1. (a) i. Evaluate the constant c (the integration can be done by MATLAB). ii. Plot the probability density function over the domain (-1,1). Is this density function skewed to the right, skewed to the left, or symmetric? (b) Use MATLAB to evaluate i. the mean p = E(X)= 1, 2f(x) dx; ii. E(X) = {1, 2} (x) dx; iii. the variance o? =Var(x) = E(X) – , and the standard deviation o. *(e) i. Use MATLAB to find an expression for the cumulative distribution function F(x). ii. Check the result in (1) by differentiation. Hint: simplify (ans) might help! iii. Evaluate P(-0.2 < X 50.2). (a) Find the median of X. Note that MATLAB provides four solutions to the polynomial equation obtained by setting F equal to 0.5, but only one of these solutions lies within the domain (1,1).