  In this work the authors consider an inverse source problem in the following
stochastic fractional diffusion equation $$\partial_t^\alpha u(x,t)+\mathcal{A}
u(x,t)=f(x)h(t)+g(x) \dot{\mathbb{W}}(t).$$ The interested inverse problem is
to reconstruct $f(x)$ and $g(x)$ by the statistics of the final time data
$u(x,T).$ Some direct problem results are proved at first, such as the
existence, uniqueness, representation and regularity of the solution. Then the
reconstruction scheme for $f$ and $g$ is given. To tackle the ill-posedness,
the Tikhonov regularization is adopted. Finally we give a regularized
reconstruction algorithm and some numerical results are displayed.
