Calculating the Expected Power Dissipated by a Resistor

Calculating the Expected Power Dissipated by a Resistor
In this exercise, we are given a scenario where a resistor is chosen uniformly at random from a box containing three resistors with values of 1 ohm, 2 ohms, and 5 ohms. The chosen resistor is then connected to a live wire carrying a current, which is an Exponential random variable with a parameter (lambda = 0.5). The current and the resistor are independent of each other.
Given:
Resistor values: 1 ohm, 2 ohms, and 5 ohms (chosen uniformly at random)
Current ( I ) is an Exponential random variable with parameter ( lambda = 0.5 )
The power dissipated by the resistor is calculated using the formula: P = I^2 R
Your task is to find the expected power dissipated by the resistor.
Statistics and Probabilty Tutorial Videos - Worked Examples and Demonstrations about Statistics