Consider the following premises. If Joseph doesn't write a letter, then it is windy. Robert is not curious. Joseph is writing a letter if and only if Robert is curious. If Joseph writes a letter, then Robert is curious. Can we infer the following from them? It is windy.
 From the fact that Joseph is writing a letter if and only if Robert is curious we can infer that if Robert were curious, then Joseph is writing a letter. From the fact that if Robert were curious, then Joseph is writing a letter, and that if Joseph writes a letter, then Robert is curious we can infer that Robert is curious if and only if Joseph is writing a letter. From the fact that Robert is curious if and only if Joseph is writing a letter, and that Robert is not curious we can infer that Joseph is not writing a letter. Finally, from the fact that if Joseph doesn't write a letter, then it is windy, and that Joseph is not writing a letter we can infer that it is windy. Therefore, the answer is yes.