Consider the following set of Stern-Gerlach experiments. In this experiment the spins ejected from the source are not random, but are in a specific quantum state ). Your job is to determine the state) from the outcomes of measuring the spin component Sr, Sy, or S. on many copies of |). The measurement outcomes are shown below. The statistics for S, are intentionally left blank. 1 10k Stop R1234 10k Stop R1234 25% 2558 75% 7695 9374 Y 716 50% 110k 5022 Stop Z R1234 50% 5088 Answer the following questions. 1. Based on the measurement data above, determine the state vector ) that describes the spin-1/2 particles exiting the source. Hint: This question involves using the Born rule in reverse. Consider which general state )=cos+)+esin-) on the Bloch sphere, or alternatively which general state |) = al+)+b), is consistent with the measured probabilities. If using the Bloch sphere, think about what the measured probabilities indicate about and of a general state) on the Bloch sphere. 2. Based on the state ) that you have inferred, what are the possible results of a measurement of the spin component Sy, and with what the probabilities do they occur? Are they consistent with the measured data? Hint: Remember that there may be some statistical fluctuations in the data due to the sample size.