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Consider the function: ;0sxs1 fx(x) = { c(2 - x) ; 1< xs 2 ; otherwise. cx Find e 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 (a) (b) above, for four regions of x: ;x < 0 ;0sxs1 ;1< xs 2 ;x 2 2 Fx(x) = What is the mean (expected value) of X? (d) What is the variance of X? (e) A median of X is a value m that splits the probability in half: 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)?

Consider the function: ;0sxs1 fx(x) = { c(2 - x) ; 1< xs 2 ; otherwise. cx Find e 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 (a) (b) above, for four regions of x: ;x < 0 ;0sxs1 ;1< xs 2 ;x 2 2 Fx(x) = What is the mean (expected value) of X? (d) What is the variance of X? (e) A median of X is a value m that splits the probability in half: 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)?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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part D and E

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 ;1< 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)?
Transcribed Image 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 ;1< 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)?
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