Let X1, X2, . . . , Xn be a random sample from an exponential distribution Exp(λ). (a) Show that the mgf of X ∼ Exp(λ) is MX(t) = (1 − λt) −1 , t < 1 λ . (b) Let the r. v. Y = 2 λ Pn i=1 Xi . Find the mgf of Y and deduce that Y ∼ χ 2 (2n). (c) Derive a 100(1 − α)% CI for λ. (d) A random sample of 15 heat pumps of a certain type yielded the following observations on lifetime (in years): 2.0 1.3 6.0 1.9 5.1 0.4 1.0 5.3 15.7 0.7 4.8 0.9 12.2 5.3 0.6 Assume that the lifetime distribution is exponential. What is a 95% CI for the true average and the standard deviation of the lifetime distribution?

angle uzt is congruent to angle tzy. angle vzw is congruent to angle yzx.

(credits to leowren)

step-by-step explanation:

idk

step-by-step explanation:

use that smart brain

ian gone lie this got me confused

step-by-step explanation:

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.