#No, this is not possible

The Investigator feat (from Unearthed Arcana: Feats for Skills) either gives you proficiency in Investigation, or doubles your proficiency bonus for Investigation checks if you were already proficient.

However, the Prodigy feat (Xanathar's Guide to Everything, p. 75) specifies:

Choose one skill in which you have proficiency. You gain expertise with that skill, which means your proficiency bonus is doubled for any ability check you make with it. The skill you choose must be one that isn’t already benefiting from a feature, such as Expertise, that doubles your proficiency bonus.

(Emphasis mine.)

So I'm afraid you cannot also pick Investigation for the Prodigy feat if you already have the Investigation feat.

Even if you were to choose the feats in the other order (Prodigy first, then Investigator), you would only add double your proficiency bonus for the reasons noted in Theik's answer. Plus both features only state that your proficiency bonus is doubled for the check, referring to your actual proficiency bonus (i.e. if your bonus is +2 then you add +4; nothing implies that you triple anything or double the already doubled number)

No, this is not possible

The Investigator feat (from Unearthed Arcana: Feats for Skills) either gives you proficiency in Investigation, or doubles your proficiency bonus for Investigation checks if you were already proficient.

However, the Prodigy feat (Xanathar's Guide to Everything, p. 75) specifies:

Choose one skill in which you have proficiency. You gain expertise with that skill, which means your proficiency bonus is doubled for any ability check you make with it. The skill you choose must be one that isn’t already benefiting from a feature, such as Expertise, that doubles your proficiency bonus.

(Emphasis mine.)

So I'm afraid you cannot also pick Investigation for the Prodigy feat if you already have the Investigation feat.

Even if you were to choose the feats in the other order (Prodigy first, then Investigator), you would only add double your proficiency bonus for the reasons noted in Theik's answer. Plus both features only state that your proficiency bonus is doubled for the check, referring to your actual proficiency bonus (i.e. if your bonus is +2 then you add +4; nothing implies that you triple anything or double the already doubled number)

#No, this is not possible

The Investigator feat (from Unearthed Arcana: Feats for Skills) either gives you proficiency in Investigation, or doubles your proficiency bonus for Investigation checks if you were already proficient.

However, the Prodigy feat (Xanathar's Guide to Everything, p. 75) specifies:

Choose one skill in which you have proficiency. You gain expertise with that skill, which means your proficiency bonus is doubled for any ability check you make with it. The skill you choose must be one that isn’t already benefiting from a feature, such as Expertise, that doubles your proficiency bonus.

(Emphasis mine.)

So I'm afraid you cannot also pick Investigation for the Prodigy feat if you already have the Investigation feat.

Even if you were to choose the feats in the other order (Prodigy first, then Investigator), you would only add double your proficiency bonus for the reasons noted in Theik's answer. Plus both features only state that your proficiency bonus is doubled for the check, referring to your actual proficiency bonus (i.e. if your bonus is +2 then you add +4; nothing implies that you triple anything or double the already doubled number)

#No, this is not possible

The Investigator feat (from Unearthed Arcana: Feats for Skills) either gives you proficiency in Investigation, or doubles your proficiency bonus for Investigation checks if you were already proficient.

However, the Prodigy feat (Xanathar's Guide to Everything, p. 75) specifies:

Choose one skill in which you have proficiency. You gain expertise with that skill, which means your proficiency bonus is doubled for any ability check you make with it. The skill you choose must be one that isn’t already benefiting from a feature, such as Expertise, that doubles your proficiency bonus.

(Emphasis mine.)

So I'm afraid you cannot also pick Investigation for the Prodigy feat if you already have the Investigation feat.

Even if you were to choose the feats in the other order (Prodigy first, then Investigator), you would only add double your proficiency bonus for the reasons noted in Theik's answer. Plus both features only state that your proficiency bonus is doubled for the check, referring to your actual proficiency bonus (i.e. if your bonus is +2 then you add +4; nothing implies that you triple anything or double the already doubled number)

#No, this is not possible

The Investigator feat (from Unearthed Arcana: Feats for Skills) either gives you proficiency in Investigation, or doubles your proficiency bonus for Investigation checks if you were already proficient.

However, the Prodigy feat (Xanathar's Guide to Everything, p. 75) specifies:

Choose one skill in which you have proficiency. You gain expertise with that skill, which means your proficiency bonus is doubled for any ability check you make with it. The skill you choose must be one that isn’t already benefiting from a feature, such as Expertise, that doubles your proficiency bonus.

(Emphasis mine.)

So I'm afraid you cannot also pick Investigation for the Prodigy feat if you already have the Investigation feat.

#No, this is not possible

The Investigator feat (from Unearthed Arcana: Feats for Skills) either gives you proficiency in Investigation, or doubles your proficiency bonus for Investigation checks if you were already proficient.

However, the Prodigy feat (Xanathar's Guide to Everything, p. 75) specifies:

Choose one skill in which you have proficiency. You gain expertise with that skill, which means your proficiency bonus is doubled for any ability check you make with it. The skill you choose must be one that isn’t already benefiting from a feature, such as Expertise, that doubles your proficiency bonus.

(Emphasis mine.)

So I'm afraid you cannot also pick Investigation for the Prodigy feat if you already have the Investigation feat.

Even if you were to choose the feats in the other order (Prodigy first, then Investigator), you would only add double your proficiency bonus for the reasons noted in Theik's answer. Plus both features only state that your proficiency bonus is doubled for the check, referring to your actual proficiency bonus (i.e. if your bonus is +2 then you add +4; nothing implies that you triple anything or double the already doubled number)