A well known experiment involving Transgenic Organisms is the ob mouse which lead to the discovery of the hormone leptin.
An example of a Transgenic Organism is Goats that produce milk containing Spider Silk to discover new production methods.
In order to get a transgenic goat, you first have to obtain an embryo donor and insert the chosen DNA into the embryo using DNA pronuclear microinjection. The microinjected embryos are then inserted into other goats which will mean that they should give birth to transgenic kids. However, there is a less than 10% chance of having transgenic kids with the DNA pronuclear microinjection. Somatic cell nuclear transfer will mean all the kids born from the goats with the reconstructed embryos will be transgenic. 
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<references/>tag was found