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Wel, yes, but you cannot use the key $k_1$ for anything else because knowledge of $k_1$ would mean that an attacker can simply calculate $k_2$. If an attacker can find a direct relation between parts of the output then the function is of course not pseudo random anymore. So although it is possible it seems pretty useless to me. Even if you would not ...


It isn't a good cryptographical PRF (and, to be fair to the inventor, he never claimed it was). Marvin32 starts with a secret state, and processing the message and the state to give a new state, and at the end, outputs the state. However, it outputs the entire state, and the state update process is invertible (if you know the message); hence if you know ...

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