A man has seven keys on a key ring, one of which fits the door he wants to unlock. He randomly selects a key and tries it. If it does not unlock the door, he randomly selects another key from those remaining and tries to unlock the door with it. He continues in this manner until the door is unlocked. Let X be the number of keys he tries before unlocking the door, counting the key that actually worked. Find the expected value and the standard deviation of X.

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