Why does Lady Catelyn want Lord Eddard to take the job as King's Hand?

Lady Catelyn wants Lord Eddard to take the job as King's Hand because she received a letter from her sister, Lysa Arryn, that suggests Jon Arryn was murdered by Robert's wife and her family. Lady Catelyn uses the information from the letter to convince Eddard to take the job so he can find out the truth about Jon Arryn's death.