1. An urn contains 4 red balls, 3 blue balls, 2 green balls and one black ball. One ball is selected at random. Consider games X defined as follows. Blue X - 85.00 +$1.00 + $2.50 + S10.00 Green Black Red (a) Find the probabilities P(X > 1.00) and P(X 2 1.00). (b) Find the expected value, E(X). (c) Find the probability standard deviation, o(X). (d) Find the cumulative distribution functions F(2) = P(X < z). 2. A cumulative distribution function of a random variable X is given as follows. 0.00, if z<-2.0, 0.30, if -2.0 s z< 1.5, F(z) = {0.85, if 1.5 Sz< 2.0, 0.90, if 2.0 sz < 3.25, 1.00, if 3.25 S I. (a) Find the probability mass function. (b) Find the probability, P(1.0
1. An urn contains 4 red balls, 3 blue balls, 2 green balls and one black ball. One ball is selected at random. Consider games X defined as follows. Blue X - 85.00 +$1.00 + $2.50 + S10.00 Green Black Red (a) Find the probabilities P(X > 1.00) and P(X 2 1.00). (b) Find the expected value, E(X). (c) Find the probability standard deviation, o(X). (d) Find the cumulative distribution functions F(2) = P(X < z). 2. A cumulative distribution function of a random variable X is given as follows. 0.00, if z<-2.0, 0.30, if -2.0 s z< 1.5, F(z) = {0.85, if 1.5 Sz< 2.0, 0.90, if 2.0 sz < 3.25, 1.00, if 3.25 S I. (a) Find the probability mass function. (b) Find the probability, P(1.0
Can you answer the last subsection D for question 1? Then answer question #2- Section A-B?
Transcribed Image Text:Math 1680 Elementary Probability and Statistics
Exercise Set 6
Name:
1. An urn contains 4 red balls, 3 blue balls, 2 green balls and one black ball. One ball is
selected at random. Consider games X defined as follows.
Red
Blue
Green
Black
-$5.00 +$1.00+ $2.50 + $10.00
(a) Find the probabilities P(X > 1.00) and P(X > 1.00).
(b) Find the expected value, E(X).
(c) Find the probability standard deviation, o(X).
(d) Find the cumulative distribution functions F(r) = P(X < x).
2. A cumulative distribution function of a random variable X is given as follows.
0.00, if r< -2.0,
0.30,
if -2.0 <r< 1.5,
F(r) = {0.85,
if 1.5 <a < 2.0,
0.90,
if 2.0 <a < 3.25,
1.00,
if 3.25 < r.
(a) Find the probability mass function.
(b) Find the probability, P(1.0 < X < 2.0).
(c) Find the expected value.
(d) Find the probability standard deviation.
3. From the urn of Problem 1, ten balls are selected at random with replacement.
(a) Estimate the probability that four or less red balls are selected.
(b) Estimate the probability that more than four blue balls are selected.
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