Let X represent the lifetime of a component, in weeks Let Y represent the lifetime of the component in days, so Y 7X Suppose X Exp() a Let FY be the cumulative distribution function of Y and let FX be the cumulative distribution function of X Show that FY (y) 1 ey 7 b Show that Y Exp( 7) ...

Let X represent the lifetime of a component, in weeks. Let Y represent the lifetime of the

Question:

Let X represent the lifetime of a component, in weeks.
Let Y represent the lifetime of the component in days, so Y = 7X. Suppose X ∼ Exp(λ).
a. Let FY be the cumulative function of Y and let FX be the cumulative function of X. Show that FY (y) = 1 − e−λy/7.
b. Show that Y ∼ Exp(λ/7).
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...