Show that the failure-rate function is given by if and only if the time to failure distribution

Question:

Show that the failure-rate function is given by if and only if the time to failure distribution is the Weibull distribution

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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...