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Cousider the following function; where m € R: '440"' 2 10 f(r) (o otherwise3 points) For which value(s) o = is f(r) probability density funetio...

Question

Cousider the following function; where m € R: '440"' 2 10 f(r) (o otherwise3 points) For which value(s) o = is f(r) probability density funetion? State the condition(s) that make f() a valid palf using the value(s) of % in the final answer. b) 2 points) Let X be a continous random variable with pdf f(1) for value(s) o = from part #)_ What is the medlian o X in terts o v? points) Find the expectation o X for m > L in terms of !. What is the expectation il m = 1/2? Hint: You C

Cousider the following function; where m € R: '440"' 2 10 f(r) (o otherwise 3 points) For which value(s) o = is f(r) probability density funetion? State the condition(s) that make f() a valid palf using the value(s) of % in the final answer. b) 2 points) Let X be a continous random variable with pdf f(1) for value(s) o = from part #)_ What is the medlian o X in terts o v? points) Find the expectation o X for m > L in terms of !. What is the expectation il m = 1/2? Hint: You C(I consider litnu-,0 U = 00 poiuts) For which values of % is the variance of X liuite? Fiud the variance for such T} in terms o 1



Answers

For probability density function, over the given interval, find $E(x), E\left(x^{2}\right),$ the mean, the variance, and the standard deviation. $$f(x)=\frac{3}{2} x^{2}, \quad[-1,1]$$

It is question. Good record on that. If we have the X follows the normal distribution with the main legal to meal and variance equal to the Sigma Square. And then that's the function will be equal to one. Over Sigma squared the two pi each of the power miners ex miners meal square over two Sigma Square for the X grade for the X between minus infinity to infinity. So x will be in the real number here and in this question were given the density FX Echo 21 on was carried on the two pi each the power minus one over two And then we have the X minus four square not to stand. It will be ready standing to the one other square root on the two pi and one times one here and then we have each other about minus 1/2 and we have this will be we can release them into the miners X minus four square over two times one so we can identify the one here. It will be the sigma here. This one will be the one squares well can run as a one square and then the far here we go to the meal. And from here we can find that the e on the X equal to the far and of, uh, standard division sigma. It goes to the square root on the friend on the X we go to the one.


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