Show that if Y1 has a chi-square distribution with v1 degrees of freedom and Y2 has a

Question:

Show that if Y1 has a chi-square distribution with v1 degrees of freedom and Y2 has a chi-square distribution with v2 degrees of freedom, then U = Y1 +Y2 has a chi-square distribution with v1 +v2 degrees of freedom, provided that Y1 and Y2 are independent.

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...