## Question

###### Cousider the following function; where m â‚¬ 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 â‚¬ 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

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