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Solved: Determine the cumulative distribution function for
Chapter 3, Problem 39E(choose chapter or problem)
Determine the cumulative distribution function for the random variable in Exercise 3-17; also determine the following probabilities:
(a) \(P(X \leq 1.25)\) (b) \(P(X \leq 2.2)\) (c) \(P(-1.1<x \leq 1)\) (d) \(P(X>0)\)
Equation transcription:
Text transcription:
P(X leq 1.25)
P(X leq 2.2)
P(-1.1<x leq 1)
P(X>0)
Questions & Answers
QUESTION:
Determine the cumulative distribution function for the random variable in Exercise 3-17; also determine the following probabilities:
(a) \(P(X \leq 1.25)\) (b) \(P(X \leq 2.2)\) (c) \(P(-1.1<x \leq 1)\) (d) \(P(X>0)\)
Equation transcription:
Text transcription:
P(X leq 1.25)
P(X leq 2.2)
P(-1.1<x leq 1)
P(X>0)
ANSWER:Solution :
Step 1 of 4:
The table is given below.
x |
-2 |
-1 |
0 |
1 |
2 |
f(x) |
0.2 |
0.4 |
0.1 |
0.2 |
0.1 |
Then the cumulative distribution function for the given data:
x |
f(x) |
F(x) |
-2 |
0.2 |
0.2 |
-1 |
0.4 |
0.2+0.4 = 0.6 |
0 |
0.1 |
0.6+0.1 = 0.7 |
1 |
0.2 |
0.7+0.2 = 0.9 |
2 |
0.1 |
0.9+0.1 = 1.0 |
The resultant cumulative distribution function for the given data is
Our goal is:
We need to determine the cumulative distribution function.
a). P(X1.25).
b). P(X2.2).
c). P(-1.1< X1).
d). P(X >0).
a). Now we have to find P(X1.25).
P(X1.25) = 0.9
Therefore, P(X1.25) = 0.9.