PDF PIECEWISE FUNCTION WITH TWO PIECES
Example:
Consider the probability density function:
  x 2  2 x,
0  x 1

f ( x)   1
 (3x  5), 1  x  a
 2
a) Determine the value of a.
b) Sketch the graph of f(x).
c) Justify that f(x) is a valid pdf.
3

d) Calculate i) P  X  
2

2

ii) P  X  
3

IB Webinar Series 2016 Calculus Bozenna Graham
d) State the mode of the distribution.
e) Find the mean.
f) Find the mode.
median = 0.832 (the only solution in the given domain)
IB Webinar Series 2016 Calculus Bozenna Graham