Summation of independent discrete random variables? We have a summation of independent discrete random variables (rvs) $Y = X_1 + X_2 + \ldots + X_n$.  Assume the rvs can take non-negative real values.  How can we find the probability mass function of $Y$?
Is there any efficient method like the convolution for integer case?

Since the random variables are continuous, you would speak of their probability density function (instead of the probability mass function). The probability density function (PDF) of $Y$ is simply the (continuous) convolution of the PDFs of the random variables $X_i$. Convolution of two continuous random variables is defined by
$$(p_{X_1}*p_{X_2})(x)=\int_{-\infty}^{\infty}p_{X_1}(x-y)p_{X_2}(y)\;dy$$
EDIT: I was assuming your RVs are continuous, but maybe I misunderstood the question. Anyway, if they are discrete then (discrete) convolution is also the correct answer.
EXAMPLE: Let $X_1$ and $X_2$ be two discrete random variables, where $X_1$ takes on values $1/2$ and $3/4$ with probabilities $0.5$, and $X_2$ takes on values $1/8$ and $1/4$ with probabilities $0.4$ and $0.6$, respectively. So we have $p_{X_1}(x)=0.5\delta(x-1/2) + 0.5\delta(x-3/4)$ and $p_{X_2}=0.4\delta(x-1/8)+0.6\delta(x-1/4)$. Let $Y=X_1+X_2$. Then $p_Y(x)$ is given by the convolution of $p_{X_1}(x)$ and $p_{X_2}(x)$:
$$p_Y(x)=0.2\delta(x-5/8)+0.3\delta(x-3/4)+0.2\delta(x-7/8)+0.3\delta(x-1)$$
