1. f[x]=3x^2
–
2x + 2 for the interval .5< x < c.
a) Find c that makes f[x] legitimate.
b) Find F[x].
c) Find the probability that X is more than .75.
d) Find the probability that X is less than .6.
e) Find E[X].
f) Find E[X^2] and then Var(X).
Let F[X] = 4x^3  12x^2 + 4x
–
2
from
2.69804806238812 < X < 2.73461011337304
g) Find f[X].
2. Let X~U(2,7)
a) Find the probability that X is between 3 and 5.
b) Find the probability that X is at most 4.
c) Find the probability that X is at least 3.
d) Find E[X].
e) Find the probability that X is at least 4.5.
f) Find Var(X).
g) Let Y~U(5,10). Find Var(Y). Does this answer surprise you?
3. Let T~Expo(lambda=5)
a) Find the probability that T is more than 4.
b) Find the probability that T is at most 2.5.
c) Find the probability that T is less than 1 but more than .2.
d) Find E[X].
e) Find Var(X).
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(Do a change of time unit problem)
4. Suppose S~ Exponential with a mean of 5 minutes.
a) What is lambda?
b) Find the probability that you will have an event (Success) before a quarter of an hour is over.
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 Fall '08
 MARTIN
 Probability

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