The joint occurrence probability of the moment capacity (M) and force (F) applied on a beam has a linear joint probability density function: f (M, F) = 3F for the interval of 0 sM s FS 1. a) Determine the marginal probability density functions of moment and force. b) Determine the expectations and variances of marginal moment and force distributions. c) Compute the covariance and correlation coefficient of moment and force. d) Comment on the degree of correlation of these random variables.

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The joint occurrence probability of the moment capacity (M) and force (F) applied
on a beam has a linear joint probability density function: f (M, F) = 3F for the interval of 0 sM SFS1.
a) Determine the marginal probability density functions of moment and force.
b) Determine the expectations and variances of marginal moment and force distributions.
c) Compute the covariance and correlation coefficient of moment and force.
d) Comment on the degree of correlation of these random variables.
Transcribed Image Text:The joint occurrence probability of the moment capacity (M) and force (F) applied on a beam has a linear joint probability density function: f (M, F) = 3F for the interval of 0 sM SFS1. a) Determine the marginal probability density functions of moment and force. b) Determine the expectations and variances of marginal moment and force distributions. c) Compute the covariance and correlation coefficient of moment and force. d) Comment on the degree of correlation of these random variables.
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