Engineering Joint probability problem

In summary, a joint probability problem in engineering involves calculating the likelihood of two or more events occurring simultaneously. To calculate joint probability, you multiply the individual probabilities of each event together. There is a difference between joint probability and conditional probability, with joint probability looking at both events together and conditional probability considering one event in relation to the other. Joint probability can be used to predict future events in engineering and is commonly used in reliability engineering to identify potential vulnerabilities and design more reliable systems.
  • #1
Spartan452
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Homework Statement



axial load in an interior column in a two-story building is a random variable Y described as the sum of the floor loads X1 and X2 the floor load each is a normally distributed random variable with a mean value of 90kn.m and a coefficient of variation of .20. The random variables X1 and X2 are independent.

A)-Compute the mean and std deviation of Y
B)-If the resistance of the column R is a normal random variate with a mean of 270KN and a coefficient of variation of .20, compute the probability of failure of the column assuming that Y and R are statistically independent


Homework Equations



Im just kinda confused on where to get started, I believe the function is continuous but I don't know what the bounds are nor do I know what the function actually looks like.
It says the function is normally distributed so I think it would be the standard normal density function phi(x-mean/std dev) and since there are two and they are independent it should be squared. I do not know what the target value is either. But i might be wrong and my approach might be totally off, my book doesn't really provide any examples on how to deal with a problem like this...

I think you have to solve b the same way you would solve for a, but I just don't know how to deal with a.

The Attempt at a Solution


This is my attempt attached here, I think it might all be wrong...
 

Attachments

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  • #2
A)-The mean of Y is the sum of the means of X1 and X2 which is 180KN.m. The std deviation of Y is the square root of the sum of the variance of X1 and X2, which is the coefficient of variation times the mean times the square root of 2, which is (0.2*90kn.m*sqrt(2))=25.45KN.mB)-The probability of failure is the integral of the product of the normal density function of Y and R from 0 to infinity. This can be simplified to the integral of the normal density function (phi) of Y and R since it is continuous from -infinity to infinity. The formula for this integral is the product of the standard normal cumulative distribution function (Phi) of Y and R evaluated at infinity minus the product of the standard normal cumulative distribution function of Y and R evaluated at 0. Phi(infinity)=1 and Phi(0)=0. Therefore, the probability of failure is 1.
 

1. What is a joint probability problem in engineering?

A joint probability problem in engineering involves calculating the likelihood of two or more events occurring simultaneously. It is commonly used in risk analysis and decision-making processes.

2. How do you calculate joint probability in engineering?

To calculate joint probability, you multiply the individual probabilities of each event. For example, if the probability of event A is 0.5 and the probability of event B is 0.3, the joint probability would be 0.5 x 0.3 = 0.15.

3. What is the difference between joint probability and conditional probability in engineering?

Joint probability involves calculating the likelihood of two events occurring together, while conditional probability involves calculating the likelihood of one event occurring given that another event has already occurred. In other words, joint probability considers both events together, while conditional probability looks at one event in relation to the other.

4. Can joint probability be used to predict future events in engineering?

Yes, joint probability can be used to predict future events in engineering. By analyzing the likelihood of two or more events occurring together, engineers can make more informed decisions and mitigate potential risks.

5. How is joint probability used in reliability engineering?

In reliability engineering, joint probability is used to calculate the probability of multiple components or systems failing simultaneously. This helps engineers identify potential vulnerabilities and design more reliable and robust systems.

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