2. Consider the function: ;0sxs1 fx(x) = { c(2 - x) ; 1 2 ... ... Fx(x) ... ... (c) What is the mean (expected value) of Xx? (d) What is the variance of X? A median of X is a value m that splits the...


part D and E


2. Consider the function:<br>;0sxs1<br>fx(x) = { c(2 - x) ; 1 < xs 2<br>; otherwise.<br>Find c to make this the PDF of a R.V. X, then plot/draw the resulting fx.<br>Calculate and express X's CDF Fx(x), the same way fx(x) is expressed<br>сх<br>(a)<br>(b)<br>above, for four regions of x:<br>;x < 0<br>;0sxs1<br>;1< xs 2<br>;x > 2<br>...<br>...<br>Fx(x)<br>...<br>...<br>(c)<br>What is the mean (expected value) of Xx?<br>(d)<br>What is the variance of X?<br>A median of X is a value m that splits the probability in half:<br>1<br>P(X s m) = P (X > m) =<br>In this problem X has one such m. Show that this median is the same as the<br>mean of X. Does it always have to be (i.e., for other R.V.s)?<br>

Extracted text: 2. Consider the function: ;0sxs1 fx(x) = { c(2 - x) ; 1 < xs="" 2="" ;="" otherwise.="" find="" c="" to="" make="" this="" the="" pdf="" of="" a="" r.v.="" x,="" then="" plot/draw="" the="" resulting="" fx.="" calculate="" and="" express="" x's="" cdf="" fx(x),="" the="" same="" way="" fx(x)="" is="" expressed="" сх="" (a)="" (b)="" above,="" for="" four="" regions="" of="" x:="" ;x="">< 0="" ;0sxs1="">< xs="" 2="" ;x=""> 2 ... ... Fx(x) ... ... (c) What is the mean (expected value) of Xx? (d) What is the variance of X? A median of X is a value m that splits the probability in half: 1 P(X s m) = P (X > m) = In this problem X has one such m. Show that this median is the same as the mean of X. Does it always have to be (i.e., for other R.V.s)?

Jun 10, 2022
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