Google·Data Scientist·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Jun 2026

Summary

Ran into a probability/stats question at Google that felt straightforward until I second-guessed myself halfway through. Short interview, one question, left not totally sure how I did.

Questions Asked (1)

If you subtract one normally distributed variable from another, where both are independent and identically distributed with mean 1 and variance 3, what distribution does the result follow?

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Author's notes

I knew the answer involved a normal distribution but fumbled the parameters for a second.

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AI HintsAI Generated

Suggested Approach

State the distribution of the difference of two independent normal variables by applying the linear combination property of normal distributions. Compute the mean and variance of the difference using the given parameters, and clearly present the final distribution.

Pro tip: Mention that independence is crucial for the variance of the difference to be the sum of variances; if they were dependent, you would need to account for covariance. Also, relate this to practical applications like A/B testing where comparing two independent groups often involves such differences.

1. Identify the distributions

Let X and Y be independent and identically distributed normal variables with mean μ = 1 and variance σ² = 3. So X ~ N(1, 3) and Y ~ N(1, 3).

2. Define the difference

We want the distribution of D = X - Y. Since X and Y are independent, D is a linear combination of independent normal variables.

3. Apply properties of normal distributions

A linear combination of independent normal variables is normally distributed. Thus, D follows a normal distribution.

4. Compute mean and variance

The mean of D is E[X] - E[Y] = 1 - 1 = 0. The variance is Var(X) + Var(Y) = 3 + 3 = 6 (since independent, variances add even for subtraction).

5. State the final distribution

Therefore, D ~ N(0, 6).

Key Points to Mention

Independence of the two variables
Normal distribution is closed under linear combinations
Mean of the difference is the difference of means
Variance of the difference is the sum of variances when independent
Resulting distribution is normal with mean 0 and variance 6
Practical relevance: e.g., in A/B testing, difference of means from independent groups

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