Stress is applied to a 20-in. Steel bar that is clamped in a fixed position at each end. Let Y be = 10 and Var(Y) = 100/7. the distance from the left end at which the bar snaps with E(Y) suppose U = Y/20 has a standard beta distribution: f(u; a, ß): = r(a+ß) α-1 น Γ(α)Γ(β) (1 −u)³-¹; 0 12). (d) Compute the probability that the bar snaps more or less than 2 in. from where you expect it to.

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Stress is applied to a 20-in. Steel bar that is clamped in a fixed position at each end. Let Y be
the distance from the left end at which the bar snaps with E(Y) = 10 and Var(Y) = 100/7.
suppose U = Y/20 has a standard beta distribution:
f(u; a, ß) =
=
[(a+ß)
г(а)г(В)
α-1
u-(1 − u)-1; 0<u<1.
(a) What are the parameters & and ß of the relevant standard beta distribution?
(b) Compute P(8 ≤ y ≤ 12).
(c) Compute P(Y > 12).
(d) Compute the probability that the bar snaps more or less than 2 in. from where you
expect it to.
Transcribed Image Text:Stress is applied to a 20-in. Steel bar that is clamped in a fixed position at each end. Let Y be the distance from the left end at which the bar snaps with E(Y) = 10 and Var(Y) = 100/7. suppose U = Y/20 has a standard beta distribution: f(u; a, ß) = = [(a+ß) г(а)г(В) α-1 u-(1 − u)-1; 0<u<1. (a) What are the parameters & and ß of the relevant standard beta distribution? (b) Compute P(8 ≤ y ≤ 12). (c) Compute P(Y > 12). (d) Compute the probability that the bar snaps more or less than 2 in. from where you expect it to.
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