From cfcd3eefcbc547a8b69d9f5830b7a27c0bdb60ce Mon Sep 17 00:00:00 2001
From: Julian T <julian@jtle.dk>
Date: Wed, 17 Feb 2021 12:35:27 +0100
Subject: Changes to prob
---
sem6/prob/m2/opgaver.md | 20 ++++++++++++++++++++
1 file changed, 20 insertions(+)
(limited to 'sem6/prob/m2')
diff --git a/sem6/prob/m2/opgaver.md b/sem6/prob/m2/opgaver.md
index a5d0cdb..0ce9c77 100644
--- a/sem6/prob/m2/opgaver.md
+++ b/sem6/prob/m2/opgaver.md
@@ -50,4 +50,24 @@ $$
## Opgave 3
+Først skal man finde $\lambda$.
+
+$$
+ \int_{0}^{\infty} \lambda e^{- \frac x {100}} \mathrm{dx} = 1 \\
+ \left[ - \lambda 100 \cdot e^{- \frac x {100}}\right]_{0}^{\infty} = 1 \\
+ \lambda \cdot 100 = 1 \\
+ \lambda = \frac 1 {100}
+$$
+
+Nu kan man sætte 50 til 150 ind.
+
+$$
+ P(50 < x \leq 150) = \int_{50}^{150} f(x) \mathrm{dx} = - e^{- \frac {150} {100}} + e^{ - \frac {50} {100}} = 0.3834
+$$
+
+Derefter kan vi tage fra 0 til 100.
+
+$$
+ P(x < 100) = \int_{0}^{100} f(x) \mathrm{dx} = - e^{- \frac {100} {100}} = - \frac 1 e
+$$
--
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