How to find the mathematical expectation of gamma function? - Training Enrollment Network

How to find the mathematical expectation of gamma function?

e(x)=∫[c,+∞)x*β^α/γ(α)*(x-c)^(α- 1)*e^[-β(x-c)]*dx(α& gt； 0，β& gt； 0)

=∫[0,+∞)(t/β+c)*β^α/γ(α)*(t/β)^(α- 1)*e^(-t)* 1/β*dt

= 1/γ(α)*∫[0,+∞){t^[(α+ 1)- 1]/β+ct^(α- 1)}e^(-t)dt

= 1/γ(α)*[ 1/β*γ(α+ 1)+cγ(α)]

= 1/γ(α)*[α/β*γ(α)+cγ(α)]

=α/β+c

Related articles

How to make good use of the results of grade inquiry?

The Influence of Mathematics on Life

Agricultural postgraduate course

Which school is good for Olympic Mathematics training in Ningbo primary school?

Which version of the textbook is used in mathematics physics for senior one in Shaanxi Province? What about math and physics in junior high school?

A wrong textbook of mathematics elective course in senior two.

How to summarize your learning methods?

In high school mathematics. E. what is it? (Not the eccentricity in conic), why is E equal to 2 1828? All I know is that π equals 3.

The answers on pages P52 and 53 of the second math classroom exercise book in grade five! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !

The charm of primary school students' writing