Let X be physical distance, measured in inches, from its anchoring point where a bicycle spoke will snap. Then X has the following probability density function: f(x)= x(1-) 169 OSXS 13 and 0 otherwise. a)What is the probability that a bicycle spoke snaps less than 3 inches from its anchoring point? b) What is the probability that X >6? c) What is the probability that 2< X < 8? d) What is the expected value of Y (E(Y)2

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Let X be physical distance, measured in inches, from its anchoring point where a bicycle spoke will snap. Then X has the following probability density function: f(x)= -
-x(1-) for
169
13
0 < x < 13 and 0 otherwise.
a)What is the probability that a bicycle spoke snaps less than 3 inches from its anchoring point?
b) What is the probability that X >6?
c) What is the probability that 2< X < 8?
d) What is the expected value of X (E(X))?
e) What is the expected value of X2 ?
f) What is the variance of X?
g) What is the standard deviation of X?
h) What is the probability that X is less than its expected value?
i) What is the expected value of X0.6 ?
j) What is the 60th percentile of X?
k) What is the probability that X is within 2 standard deviations of its expected value?
I) What is the probability that X = 8?
Transcribed Image Text:Let X be physical distance, measured in inches, from its anchoring point where a bicycle spoke will snap. Then X has the following probability density function: f(x)= - -x(1-) for 169 13 0 < x < 13 and 0 otherwise. a)What is the probability that a bicycle spoke snaps less than 3 inches from its anchoring point? b) What is the probability that X >6? c) What is the probability that 2< X < 8? d) What is the expected value of X (E(X))? e) What is the expected value of X2 ? f) What is the variance of X? g) What is the standard deviation of X? h) What is the probability that X is less than its expected value? i) What is the expected value of X0.6 ? j) What is the 60th percentile of X? k) What is the probability that X is within 2 standard deviations of its expected value? I) What is the probability that X = 8?
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