Each front tire of a vehicle is supposed to be filled to a pressure of 26 psi. Supposethe actual air pressure in each tire is a random variable, X for the right tire and Y for theleft tire, with joint pdf- {*(x² +[K(x² + y²) 20≤x≤ 30, 20 ≤ y ≤ 300otherwisef(x, y) =a. Find the value of K.b.What is the probability that both tires are fully filled, that is, P(X ≥ 26 and Y≥ 26)?c. Determine the marginal distribution function of X.d.Are X and Y independent random variables?

As per bartleby guidelines we can solve only first three subparts and rest can be reposted

Answered: a. Find the value of K. o. What is the…

a. Find the value of K. o. What is the probability that both tires are fully filled, that is, P(X≥ 26 and Y≥26)? c. Determine the marginal distribution function of X.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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Question

Each front tire of a vehicle is supposed to be filled to a pressure of 26 psi. Suppose
the actual air pressure in each tire is a random variable, X for the right tire and Y for the
left tire, with joint pdf
- {*(x² +
[K(x² + y²) 20≤x≤ 30, 20 ≤ y ≤ 30
0
otherwise
f(x, y) =
a. Find the value of K.
b.
What is the probability that both tires are fully filled, that is, P(X ≥ 26 and Y≥ 26)?
c. Determine the marginal distribution function of X.
d.
Are X and Y independent random variables?

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