Why was the blood from the Korbon placed inside(Rashi:Yud Beis,Yud Gimmel) and not outside ?
Text of Rashi:
והיה הדם לכם לאת: לכם לאות ולא לאחרים לאות מכאן שלא נתנו הדם אלא מבפנים
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I think the simple Pshat is that the blood on the door post was for the Jewish people. It was for them to realize that it is because of adherence to this Mitzvah of Korbon Pesach that they are being spared.
The main thrust of the Korbon Pesach (see Ramban, Rambam) is a repudiation of Idolatry. These animals were worshiped as God's by the Egyptians. We rejected idolatry and accepted the one true creator of the universe Hashem. It is only through our rejection of this false philosophy and adherence to the truth and fulfillment of this command were we spared.
The reason for smearing the blood on the inside of the door-post was symbolic of coming to the understanding of the importance of self-sacrifice in the privacy of ones own home. There must be a focus on the inner dimensions of ones personality. The essence of Yiddishkite is not on the public stage, but the the inner struggle with the Yetzer Hara.As the only audience we attach significance too should be Hashem. Hence the Blood, which represents sacrifice must be on the inside, representing the Inner struggle against the Yetzer Hara and for Hashem.