Need help with Beta and Gamma distribution (MATLAB)

[Majix]

Hello. I need help with understanding matlab algorithm with beta and gamma distribution.
1) Algorithm with Beta distibution (MATLAB):

function [expected, phat]=bayes_beta_beta(prior_proportions,successes,trials)
phat=betafit(prior_proportions);
alpha = phat(1);
beta = phat(2);
expected=(successes+alpha)./(trials+beta+alpha);
end

My question - how did we get expected value this way? In Wikipedia expected value of Beta distribution - alpha/(alpha+beta).
2) Algorithm with Gamma distibution (MATLAB):

function [expected, phat]=bayes_gamma_expo(prior_data,sample,valid_n)
phat=gamfit(prior_data);
alpha = phat(1);
beta = phat(2);
expected=1./((alpha+valid_n)./(1/beta+sample));
end

My question is same - how did we get this strange formula for expected values? Sorry if my questions is silly. I'll be glad to any materials or tips about my questions.

 

[Deleted member 4993]

Hello. I need help with understanding matlab algorithm with beta and gamma distribution.
1) Algorithm with Beta distibution (MATLAB):

function [expected, phat]=bayes_beta_beta(prior_proportions,successes,trials)
phat=betafit(prior_proportions);
alpha = phat(1);
beta = phat(2);
expected=(successes+alpha)./(trials+beta+alpha);
end

My question - how did we get expected value this way? In Wikipedia expected value of Beta distribution - alpha/(alpha+beta).
2) Algorithm with Gamma distibution (MATLAB):

function [expected, phat]=bayes_gamma_expo(prior_data,sample,valid_n)
phat=gamfit(prior_data);
alpha = phat(1);
beta = phat(2);
expected=1./((alpha+valid_n)./(1/beta+sample));
end

My question is same - how did we get this strange formula for expected values? Sorry if my questions is silly. I'll be glad to any materials or tips about my questions.

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