exercise:C28d5af411: Difference between revisions

Latest revision as of 18:42, 8 May 2023

An insurance company insures a good driver and a bad driver on the same policy. The table below gives the probability of a given number of claims occurring for each of these drivers in the next ten years.

Number of Claims	Probability for the good driver	Probability for the bad driver
0	0.5	0.2
1	0.3	0.3
2	0.2	0.4
3	0.0	0.1

The number of claims occurring for the two drivers are independent.

Calculate the mode of the distribution of the total number of claims occurring on this policy in the next ten years.

0
1
2
3
4

@@ Line 1: / Line 1: @@
-An insurance company sells automobile liability and collision insurance. Let <math>X</math> denote the percentage of liability policies that will be renewed at the end of their terms and <math>Y</math> the percentage of collision policies that will be renewed at the end of their terms. <math>X</math> and <math>Y</math> have the joint cumulative distribution function
+An insurance company insures a good driver and a bad driver on the same policy. The table below gives the probability of a given number of claims occurring for each of these drivers in the next ten years.
-<math display = "block">
+{| class="table table-bordered"
-F (x,y) = \frac{xy(x+y)}{2,000,000}, \, 0 ≤ x ≤ 100, \, 0 ≤ y ≤ 100.
+|-
-</math>
+! Number of Claims !! Probability for the good driver !! Probability for the bad driver
+|-
+| 0|| 0.5 || 0.2
+|-
+| 1 || 0.3 || 0.3
+|-
+| 2 ||  0.2 || 0.4
+|-
+| 3 || 0.0  || 0.1
+|}
-Calculate <math>\operatorname{Var}(X).</math>
+The number of claims occurring for the two drivers are independent.
+Calculate the mode of the distribution of the total number of claims occurring on this policy in the next ten years.
 <ul class="mw-excansopts">
-<li>764</li>
+<li>0</li>
-<li>833</li>
+<li>1</li>
-<li>3402</li>
+<li>2</li>
-<li>4108</li>
+<li>3</li>
-<li>4167</li>
+<li>4</li>
 </ul>
 {{soacopyright | 2023}}