In $1997,$ Olga and Helen, both in their $70$s$,$ befriended Paul, a homeless man in Los Angeles. They found him an inexpensive studio apartment and paid the rent for him. They also regularly purchased groceries and clothes for him. In November of $1999,$ poor Paul was killed by a hit and run driver in an alley near West Hollywood. In $2003,$ Olga and Helen also befriended Ken, another homeless man in Los Angeles. They found him an inexpensive studio apartment and paid the rent for him. They also regularly purchased groceries and clothes for him. In June of $2005,$ poor Ken was killed by a hit and run driver in an alley in West Los Angeles. Olga and Helen had taken out numerous life insurance policies on both Paul and Ken naming themselves as the beneficiaries $($entitled to receive the insurance proceeds on the death of the insured$)$ providing total life insurance proceeds of many hundreds of thousands of dollars. $($Paul and Ken had willingly signed the insurance applications. In $2006,$ Olga and Helen were charged with the murder of Paul and Ken. They were tried in $2008$ and convicted of murder and both were sentenced to life in prison.

Based on these facts answer the following questions:

Are Olga and Helen legally entitled to collect the life insurance proceeds under the policies they obtained on the lives of Ken and Paul? What is the governing legal principle? Explain.