# Clarification about inequality in summation

In my work I am facing the following situation, wherein I am trying to compute CDF of random variable $$Y$$ such that

$$F_Y(y) = \text{Pr}(\sum_{m = 1}^M |Z_m|^2\leq \frac{y}{A})$$ -----(1)

where $$Z$$ is a random variable, $$y$$ is dummy variable, $$A$$ is a constant and $$m$$ is index of summation.

My query is can we write eq. (1) as shown below in eq. (2)

$$F_Y(y) = \text{Pr}(\sum_{m = 1}^M |Z_m|\leq \sqrt{\frac{y}{A}})$$ -----(2)

Any help in this regard will be highly appreciated.

• Can we do like this as mentioned in question .....Any help will be greatly appreciated.... May 23 at 6:41