🚀 The feature, motivation and pitch

Current lack of type hints causes some issues, for instance #76772

• Add type hints for lazy_property class ([typing] Add type hints to @property and @lazy_property in torch.distributions. #144110)
• Add type hints for @property and @lazy_property ([typing] Add type hints to @property and @lazy_property in torch.distributions. #144110)
• Add type hints to __init__ methods ([typing] Add type hints to __init__ methods in torch.distributions. #144197)
• Add type hints to methods (Full static typing for torch.distributions #144219)
• Add type hints to attributes (Full static typing for torch.distributions #144219)
• Add type hints to utility functions (Full static typing for torch.distributions #144219)

Alternatives

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Additional context

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cc @fritzo @neerajprad @alicanb @nikitaved @ezyang @malfet @xuzhao9 @gramster