Brian conducts a study to examine the ability of boys and girls in solving difficult mathematical problems. he expects girls to perform much better than boys and communicates his expectation to the participants in a subtle manner. this is an example

Experimenter bias.

Explanation: Experimenter bias is the condition which describes a person as a part of experiment who is influencing the outcome of the experiment so that the desired or preferred results can be obtained.Experimenter bias is also known as research biasing.

The example mentioned in the question where Brian is conducting the study with sharing his views with the participants that he expects girls should perform better than boys in the experiment is example of experimenter bias.

The actual experiment should have been conducted without any thought sharing or acknowledgement which would have produced unbiased outcomes.But according to Brain's study, the expectations are conveyed ,therefore it will influence the result of the experiment as it becomes biased.