Math  /  Data & Statistics

QuestionFor the joint probability density function f(x,y)=f(x, y)= 2x+2y90\frac{2 x+2 y}{90} for 1x4&1y41 \leq \mathrm{x} \leq 4 \& 1 \leq \mathrm{y} \leq 4, and f(x,y)=0\mathrm{f}(\mathrm{x}, \mathrm{y})=0 elsewhere
Find P(1<X<2,3<Y<4)P(1<X<2,3<Y<4) (Write in the form of an integer or decimal)
Answer: \square

Studdy Solution
Calculate the result of the outer integral:
=(2290+7290)(1290+7190)= \left( \frac{2^2}{90} + \frac{7 \cdot 2}{90} \right) - \left( \frac{1^2}{90} + \frac{7 \cdot 1}{90} \right)
=(490+1490)(190+790)= \left( \frac{4}{90} + \frac{14}{90} \right) - \left( \frac{1}{90} + \frac{7}{90} \right)
=1890890= \frac{18}{90} - \frac{8}{90}
=1090=19= \frac{10}{90} = \frac{1}{9}
The probability is:
19 \boxed{\frac{1}{9}}

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord