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

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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?