Question

2. In a toxicology experiment, Y denotes the death time in minutes) for a single rat treated with a certain toxin. The probability density function (pdf) for Y is given by fy (v) = Tey, y> 0, 0, otherwise. (a) Derive the cumulative distribution function (cdf) of Y. (b) Find the probability that this rat survive more than 2 minutes. (c) Find the expected death time for this rat. (d) Find the variance of Y. (e) Find the mgf of Y. (f) Find Ele-Y) (g) Find E(Y3). (h) Find E(VY).

Answer 1

Y denoles the death time, cin minutes) for a single not treated with a certain tovin The probability density function is, түсу) = fe2 уто goo Jo 0.w (a) Commulative distribution function offis Fly) = { fog, dag = seg dy = -6y teo Fly) = 1-6-y (2) The probability that this not surive more than a minutes is, PIX72) = 1 - P(x52) :! - F(2) -1-(1-e-?) 31-1te-2 -0-2 P(x)2) = 0.1353

The probability that this at survive more than 2 minutes is 0.1353 (c) The Expected death time for this rats Ely): Sy fesley - Ру е-Уду Seyyidly Bingolog.com : 12 :(2-1)! =1? [F(y) = 1 ] (a) variance of r is FC42) = 5 942 fcy) dy - f yo pry dy = Seyya'dy -00 Teory on dy

- (3-1) ! - 21 - 21 SE(y) = 2 [(۷) ع - (92) - (لا)۱ ل - 2 - له : (لا)iv y is, (1) The mgf of ۴۱ (4) = F (e) - sety fcy) dy = ولى اتم وام ویلا (1-1)- دولار 1- 1)- : [ ا را په (11) - ا : [1+ 5- ل - ا * (ب) و |

وك (y) ؟ لا-حا: (۹- م ) (4) | وأما و لا علاج هه وه د لار لا- لاتم : pe?y dy I dy : دعا ] - [ (+1] : : (لام)E] (g) Find Elus) وله (9) 3 - (۹۹) رهاب التي دل - boery goodly کو 9ی پا - : :(-۱۱| لي : (3)