Question 3. Suppose the random variable
Zhas the following probability density function,
f_(Z)(x), described below:
f_(Z)(x)={((x-1)/(8) if 1<=x<=3),((1)/(8) if 4<=x<=6),(8-x if 7<=x<=8),(0 otherwise ):}The graph of
f_(Z)(x)is displayed below.
f_(z)(x)(93w 2 of 3 (a) Use the graph of
f_(Z)(x)above and properties of probability to calculate
P(2<=Z<=(15)/(2)). Show all your workings and express your final answer as a fraction in its simplest form. (b) Let
F_(Z)(x)denote the cumulative (probability) distribution function for
Zwhere
Zis the random variable whose probability density function,
f_(Z)(x), is described above. Determine and write down the cumulative distribution function for
Z. Show all your workings.