If in a distribution each x is replaced by corresponding value of `f(x)`, then the probability of getting `f(x)`, when the probability of getting `x_(i) is p_i`, is.

Options

A. `p_i`
B. `f(p_i)`
C. `f((1)/(p_i))`
D. none of these

Answer

To solve the problem, we need to understand the relationship between the probabilities of the original values \( x_i \) and their corresponding transformed values \( f(x_i) \).

### Step-by-Step Solution:

1. **Understanding the Given Information**:
We are given that the probability of getting \( x_i \) is \( p_i \). This means for each value \( x_i \) in our distribution, there is a corresponding probability \( p_i \).

**Hint**: Identify what \( p_i \) represents in the context of the distribution.

2. **Replacing \( x_i \) with \( f(x_i) \)**:
The question states that each \( x \) is replaced by its corresponding value \( f(x) \). Thus, we need to consider the new values \( f(x_i) \) instead of \( x_i \).

**Hint**: Think about how the transformation \( f(x) \) affects the values but not the probabilities.

3. **Analyzing the Probability of \( f(x_i) \)**:
When we replace \( x_i \) with \( f(x_i) \), we need to determine the probability of obtaining \( f(x_i) \). However, the transformation does not change the underlying favorable cases. The number of favorable outcomes for \( f(x_i) \) remains the same as that for \( x_i \).

**Hint**: Consider the nature of probability and how it is defined in terms of favorable outcomes.

4. **Conclusion**:
Since the favorable cases remain unchanged, the probability of getting \( f(x_i) \) is still \( p_i \). Therefore, we conclude that:

\[ P(f(x_i)) = p_i \]

**Hint**: Reflect on the principle that the probabilities associated with outcomes do not change when we apply a function to the outcomes.

### Final Answer:
The probability of getting \( f(x) \) when the probability of getting \( x_i \) is \( p_i \) is \( p_i \).