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 :

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