Question
The error in temperature reactivity, in degrees Celsius, of a controlled laboratory experiment, has the following cumulative distribution function F: F(x) = 0 for x
The error in temperature reactivity, in degrees Celsius, of a controlled laboratory experiment, has the following cumulative distribution function F:
F(x) = 0 for x < -1 and F(x)=x3+1
9
for -1x2 and F(x) = 1 for x > 2
a) What is the probability density function for X for -1x2?
f(x) =x2
3
f(x) =x3
f(x) =1
3
f(x) =3x2+1
9
f(x) =x4
36
b) What is the probability that X > 1?
c) What is the probability X < 1 ?
d) What is the probability that X < 0 ?
e) What is the probability that X < -0.5 ?
f) What is the probability that X < -0.5 given that X < 0?
g) Calculate the median of X.
h) What is the expected value of X?
i) What is the expected value ofX2
?
j) What is the variance of X?
k) What is the probability that X is more than 0.1 above its expected value?
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