Question

The total future years of productivity, X, of a draft round 1, of a major league baseball player has the density function: f(x)= x'e-* for OSXS and 0 otherwise. a)What is the probability that the player lasts no more than 5 years? b) What is the probability that X > 5? c) What is the probability that 3< x < 9? d) What is the expected future years of productivity, X, of a round 1 draft pick, of a major league baseball player?(E(X)) e) What is the expected value of x?? f) What is the variance of X? g) What is the standard deviation of X? h) What is the probability that X is more than 1 standard deviation below its expected value? i) What is the median of X? ) What is the probability that X is within 2 standard deviations of its expected value? k) What is the probability that X = 6?

Answer 1

Although, the value of inteGral has been provided in the beginning of the solution, but manual calculations will be too lengthy. All the value has been found using calculator. Thank you

8 5040 * (&dx-- 127+ 726+423+2108 +84023 +2520 *2 +50402 +5046) e 5040 (using integration by parts), @ P(x<5). Como tedx = 0,1334) OP(x5)1-PCX<5)= 10.8666 PCB<x<9)-s Somoze da -10.6642] Exo-fier souoste che=18] @EL) Ser. Soyo té dx = 172 vare(x) 3. ELR)-ECX)? 72-64-[B] & std. dev = 18 = 282 = 2.8284 P(X-ECX)< -0) = P(x<8-282) 18 2 Vasto tedx = 10.4519 ☺ o x7 e² de 0.5 m = 7.6692 2 5040 P(x-4320)= P(8-4823x581413) point out the = 10.95901 ® je trendo dar 101