1. **Problem Statement:** We have 4 equi-probable discrete input states $x_1=35$, $x_2=65$, $x_3=95$, $x_4=125$ and 3 equi-probable noise values $\eta_1=5$, $\eta_2=10$, $\eta_3=15$. We want to analyze the combined effect of input and noise. 2. **Understanding the Problem:** Each input $x_i$ can be combined with each noise $\eta_j$ to produce an output $y_{ij} = x_i + \eta_j$. Since both inputs and noises are equi-probable, each pair $(x_i, \eta_j)$ has probability $\frac{1}{4} \times \frac{1}{3} = \frac{1}{12}$. 3. **Calculate all possible outputs:** - For $x_1=35$: $y_{11}=35+5=40$, $y_{12}=35+10=45$, $y_{13}=35+15=50$ - For $x_2=65$: $y_{21}=65+5=70$, $y_{22}=65+10=75$, $y_{23}=65+15=80$ - For $x_3=95$: $y_{31}=95+5=100$, $y_{32}=95+10=105$, $y_{33}=95+15=110$ - For $x_4=125$: $y_{41}=125+5=130$, $y_{42}=125+10=135$, $y_{43}=125+15=140$ 4. **Summary:** The output values are $\{40,45,50,70,75,80,100,105,110,130,135,140\}$ each with probability $\frac{1}{12}$. 5. **Interpretation:** This represents the discrete output distribution of the channel with additive noise. **Final answer:** The output values and their probabilities are as above.