Notes #7 Invers e Trig Function s
Do Now:
1.
Example: Let/ and g be functions that are differentiable everywhere. If g is the inverse function of/ and g (-2) = 5. and
2'
A 2
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- ~*2.
B
E -2
D -i
In pre-calculus you should have learned that a fu

1)
X is a uniform random variable. i.e. the density of X is constant, denoted by C. If
X takes on value between 1 and 3, find
a)
Answer:
the value of C. Then give the probability density curve of X.
Base Height 3 1 C 1 Therefore, C = 1/2 or 0.5.
density
C

Review of probability:
1)
Given: P A =0.2, P B =0.4. Events A and B are independent. Find:
a) P A C
2)
c) P A B
d) P A B
e)
P A B
Given: P A =0.2, P B =0.4. Events A and B are mutually exclusive. Find:
a) P A C
3)
b) P B C
b) P B C
c) P A B
d) P A

1)
There are 14 balls in a bowl (5 blue balls, 4 red balls, 3 green balls and 2 yellow
balls). 4 balls are randomly chosen with replacement. Let X = the number of red balls
observed.
Note: X is binomial with n = 4, p = 4/14, q = 10/14 as there are 4 red b

Review of Discrete Random Variable:
Most of the steps/calculations are not given, but you have to show all the works in the
test.
1)
A dice is rolled two times and the two numbers are observed. Let X=the sum of
the two numbers.
a)
Construct a table and a

1)
X is a uniform random variable. i.e. the density of X is constant, denoted by C. If
X takes on value between 1 and 3, find
2)
a)
the value of C. Then give the probability density curve of X.
b)
P X 2
c)
P 1.5 X 2
d)
P X 4
e)
P X 0
X is a uniform ran

1)
There are 14 balls in a bowl (5 blue balls, 4 red balls, 3 green balls and 2 yellow
balls). 4 balls are randomly chosen with replacement. Let X = the number of red balls
observed.
2)
a)
Construct a table for the probability distribution of X
b)
Using t

HW 6:
1)
In a shooting competition, probability that player A hits a target in one shot is
85%. Player A is given 16 shots in the competition. Assume each shot is independent to
each other. Let X = the number of targets hit.
a)
b)
Find the following proba

Review of Random Variable:
1)
A dice is rolled two times and the two numbers are observed. Let X = the sum of
the two numbers.
a)
Construct a table and a histogram for the probability distribution of X.
b)
Compute E X
c)
Compute E X 2
2)
Even Box 1 conta

HW 8:
1)
75 students are randomly chosen from a school and the average test score is 84
with standard deviation of 14.
a)
Construct a 95% confidence interval for (the average score of all
students).
b)
Can we conclude the average test score is above 80 wi

HW5:
1)
Odd Box 1 contains numbers: cfw_1, 3, 5, 7 and Odd Box 2 contains numbers:
cfw_3, 5, 7, 9. One number is randomly chosen from the Odd Box 1 and another number
is randomly chosen from the Odd Box 2
Event A: Both numbers are less than 6
Event B: The

Review of probability:
1)
Given: P A =0.2, P B =0.4. Events A and B are independent. Find:
a) P A C =0.8 b) P B C =0.6 c) P A B =0.08 d) P A B =0.52 e)
2)
P A B =0.2
Given: P A =0.2, P B =0.4. Events A and B are mutually exclusive. Find:
a) P A C =0.8 b)