Week 21 - Probability Theory, Conditional Probability, Bayes Theorem,
Independence
Section 6.5
TEST PREPARATION PROBLEMS
1) By adding up probabilities of the individual outcomes, we nd that
Pr(A) = 0.9, Pr(B) = 0.6, and Pr(A B) = Pr(cfw_0, 2) = 0.6.
Now w
Week 22 - PDFs and CDFs, Measures of Center and Spread
Section 6.7
TEST PREPARATION PROBLEMS
7. f (x) = 2x for 0 x 1. The expected value can be written in several forms, E(X), or
X, but will be calculated as
b
E(X) = X =
xf (x) dx
a
1
=
x(2x) dx
0
1
2x2 d
Week 22 - PDFs and CDFs, Measures of Center and Spread
Section 6.9
TEST PREPARATION PROBLEMS
7. The variable has the distribution
10
0
x=
This gives a mean of X = 10
MAD(x) =
Var(x) =
Std dev.(x) =
1
3
+0
with probability
with probability
2
3
=
10
3
1
3
1
Week 22 - PDFs and CDFs, Measures of Center and Spread
Section 6.8
TEST PREPARATION PROBLEMS
5. The histogram is symmetric around the peak at 5, so the mean, median and mode are
equal to 5.
6. The histogram is symmetric aroun the peak at 5, so again the m
Week 21 - Probability Theory, Conditional Probability, Bayes Theorem,
Independence
Section 6.3
SUGGESTED PROBLEMS
1) A B = cfw_0, 2, A B = cfw_0, 1, 2, 4, Ac = cfw_3, 4
2) A B = cfw_0, 2, A B = cfw_0, 1, 2, 4, 5, Ac = cfw_3, 4, 5
3) A B = cfw_2, A B = cfw
Week 21 - Probability Theory, Conditional Probability, Bayes Theorem,
Independence
Section 6.4
SUGGESTED PROBLEMS
1) One possibility is A = cfw_0, 1, B = cfw_2, 3, 4
2) One possibility is A = cfw_0, 1, B = cfw_2, 3, C = cfw_4.
3) One possibility is A = cf
Week 23 - Statistics for Spread; Binomial Distribution
Additional Problems
TEST PREPARATION PROBLEMS
1. Normal and Binomial similarities
(a) We compare all of the values to the products np and n(1 p) to see if they are larger
than 10.
i.
ii.
iii.
iv.
If p
Week 23 - Statistics for Spread; Binomial Distribution
Section 7.5
TEST PREPARATION PROBLEMS
1. p = 3 = 0.75 for a tall plant in a single ospring. The probability of 3 out of 4 tall
4
ospring =
4
b(3; 4, 0.75) =
(0.75)3 (0.25)1 0.4219
3
2. The probability
Week 22 - PDFs and CDFs, Measures of Center and Spread
Section 6.6
SUGGESTED PROBLEMS
For questions 1-4, the table of probabilities is
# mut. Exp A Exp B Exp C Exp D
0
0.1
0.6
0.3
0.1
1
0.2
0.3
0.2
0.3
2
0.3
0.1
0.2
0.1
3
03
0.0
0.2
0.4
4
0.1
0.00
0.1
0.1
Week 21 - Probability Theory, Conditional Probability, Bayes Theorem,
Independence
Section 6.2
TEST PREPARATION PROBLEMS
11) All the AA ospring (0.25) + one fourth of the heterozygous ospring (0.25 0.5) gives
0.25 + 0.125 = 0.375. Alternatively, we know t
Week 24 - Poisson Distribution; Probability Applications
Section 7.4
TEST PREPARATION PROBLEMS
15. rate is = 0.3 mol/sec, and we observe for 3 seconds, so we will see, on average =
(0.3)(3) = 0.9 molecules leaving every 3 seconds.
The expectation/mean and