Suppose X and Y are independent random variables and that X~ on (2,5). Calculate the probability that 2X + Y < 8. Exp(14) and Y is uniformly distributed Proposed solution: Because X and Y are independent, the joint p.d.f. is given by the product of the p.d.f. of X and of Y,
Suppose X and Y are independent random variables and that X~ on (2,5). Calculate the probability that 2X + Y < 8. Exp(14) and Y is uniformly distributed Proposed solution: Because X and Y are independent, the joint p.d.f. is given by the product of the p.d.f. of X and of Y,
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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Please check if the proposed solution is corrected
![Suppose X and Y are independent random variables and that X ~ Exp(14) and Y is uniformly distributed
on (2,5). Calculate the probability that 2X + Y < 8.
Proposed solution:
Because X and Y are independent, the joint p.d.f. is given by the product of the p.d.f. of X and of Y,
that is
The desired probability is
10
r8-y
P(2X + Y <8) To fo
=
fx,y(x, y) =
=
3
e
-14s dsdt
-14x
{fo-te
x>0, y > 0
otherwise.
10
e-140 100
I
14
8-t
dt
=
[-
е
3
•10
14
14
₁ (1 - e-14 (8-1)dt = 1/2 [ 1 - 11e-14(8-1)] 10
3
4
= 28-
1
-56
-(e-
14
- e-28).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a42504d-f572-4a8c-acec-8d504fa953af%2F1b4f6d57-2fb0-467e-b6cf-6eb55175288a%2Fvz3osy_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose X and Y are independent random variables and that X ~ Exp(14) and Y is uniformly distributed
on (2,5). Calculate the probability that 2X + Y < 8.
Proposed solution:
Because X and Y are independent, the joint p.d.f. is given by the product of the p.d.f. of X and of Y,
that is
The desired probability is
10
r8-y
P(2X + Y <8) To fo
=
fx,y(x, y) =
=
3
e
-14s dsdt
-14x
{fo-te
x>0, y > 0
otherwise.
10
e-140 100
I
14
8-t
dt
=
[-
е
3
•10
14
14
₁ (1 - e-14 (8-1)dt = 1/2 [ 1 - 11e-14(8-1)] 10
3
4
= 28-
1
-56
-(e-
14
- e-28).
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