What is the expected value of a zero-coupon bond, that is: Under the following dynamics: What distribution

Question:

What is the expected value of a zero-coupon bond, that is:

Under the following dynamics:

What distribution does the zero-coupon bond follow?
Consider the distribution of ˆ«st rudu ‰ˆ ˆ‘rudu. In addition you are given that:

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...