Let f (x) = 1/2, 0 < x < 1 or 2 < x < 3, zero elsewhere, be the pdf of X.

(a) Sketch the graph of this pdf.

(b) Define the cdf of X and sketch its graph.

(c) Find q1 = π0.25.

(d) Find m = π0.50. Is it unique?

(e) Find q3 = π0.75.

Answer:

Step 1 of 6:

Let the pdf of ‘x’ is

Step 2 of 6:

a). We need to sketch the graph of this pdf.

Then, the graph of the pdf is

Step 3 of 6:

b). To define the cdf of X and to sketch the graph.

The cdf of X is

F(x) =

F(x) =

Splitting the limits

The graph of cdf is