Solution Found!
Let the random variable X have the pdf f (x) =2(1 ? x), 0
Chapter 3, Problem 9E(choose chapter or problem)
Problem 9E
Let the random variable X have the pdf f (x) =2(1 − x), 0 ≤ x ≤ 1, zero elsewhere.
(a) Sketch the graph of this pdf.
(b) Determine and sketch the graph of the cdf of X.
(c) Find (i) P(0 ≤ X ≤ 1/2), (ii) P(1/4 ≤ X ≤ 3/4),
(iii) P(X = 3/4), and (iv) P(X ≥ 3/4).
Questions & Answers
QUESTION:
Problem 9E
Let the random variable X have the pdf f (x) =2(1 − x), 0 ≤ x ≤ 1, zero elsewhere.
(a) Sketch the graph of this pdf.
(b) Determine and sketch the graph of the cdf of X.
(c) Find (i) P(0 ≤ X ≤ 1/2), (ii) P(1/4 ≤ X ≤ 3/4),
(iii) P(X = 3/4), and (iv) P(X ≥ 3/4).
ANSWER:
Answer :
Step 1 of 3 :
Given,
The random X have the probability density function f(x) = 2(1 - x) , 01
- The claim is to find the pdf and sketch the graph.
Where, the limits are lies between 0 to 1
Let us consider the x = 0, 0.25 , 0.50, 0.75 and 1
Then the pdf is
x |
f(x) = 2(1 - x) |
0 |
2 |
0.25 |
1.5 |
0.5 |
1 |
0.75 |
.5 |
1 |
0 |
From Excel
> insert the data in excel sheet
> select the data
> go to insert option
> select the chart
