Creating a discrete probability distribution: A venture
capitalist, willing to invest $1,000,000, has three investments to
choose from.
The first investment, a social media company, has a 20% chance of
returning $7,000,000 profit, a 30% chance of returning no profit,
and a 50% chance of losing the million dollars.
The second company, an advertising firm has a 10% chance of
returning $3,000,000 profit, a 60% chance of returning a $2,000,000
profit, and a 30% chance of losing the million dollars.
The third company, a chemical company has a 40% chance of returning
$3,000,000 profit, a 50% chance of no profit, and a 10% chance of
losing the million dollars.
a. Construct a Probability Distribution for each investment. This
should be 3 separate tables (See the instructors video for how this
is done) In your table the X column is the net amount of
profit/loss for the venture capitalist and the P(X) column uses the
decimal form of the likelihoods given above.
b. Find the expected value for each investment.
c. Which investment has the highest expected return?
d. Which is the safest investment and why?
e. Which is the riskiest investment and why?
When you are finished with your Assignment, upload the completed
file below. You can create a spreadsheet with all of the above and
submit it.
In: Statistics and Probability
Choosing Lottery Numbers: In the Super-Mega lottery there are 50 numbers (1 to 50), a player chooses ten different numbers and hopes that these get drawn. If the player's numbers get drawn, he/she wins an obscene amount of money. The table below displays the frequency with which classes of numbers are chosen (not drawn). These numbers came from a sample of 180 chosen numbers.
Chosen Numbers (n = 180)
| 1 to 10 | 11 to 20 | 21 to 30 | 31 to 40 | 41 to 50 | |
| Count | 43 | 54 | 27 | 33 | 23 |
The Test: Test the claim that all chosen numbers
are not evenly distributed across the five classes. Test this claim
at the 0.01 significance level.
(a) The table below is used to calculate the test statistic.
Complete the missing cells.
Round your answers to the same number of decimal places as
other entries for that column.
| Chosen | Observed | Assumed | Expected | ||||
| i | Numbers | Frequency (Oi) | Probability (pi) | Frequency Ei |
|
||
| 1 | 1 to 10 | 0.2 | 36.0 | 1.361 | |||
| 2 | 11 to 20 | 54 | 36.0 | 9.000 | |||
| 3 | 21 to 30 | 27 | 0.2 | 2.250 | |||
| 4 | 31 to 40 | 33 | 0.2 | 36.0 | |||
| 5 | 41 to 50 | 23 | 0.2 | 36.0 | 4.694 | ||
| Σ | n = 180 | χ2 = | |||||
(b) What is the value for the degrees of freedom?
(c) What is the critical value of
χ2
? Use the answer found in the
χ2
-table or round to 3 decimal places.
tα =
(d) What is the conclusion regarding the null hypothesis?
reject H0fail to reject H0
(e) Choose the appropriate concluding statement.
We have proven that all chosen numbers are evenly distributed across the five classes.The data supports the claim that all chosen numbers are not evenly distributed across the five classes. There is not enough data to support the claim that all chosen numbers are not evenly distributed across the five classes.
In: Statistics and Probability
Choosing Lottery Numbers: In the Super-Mega lottery there are 50 numbers (1 to 50), a player chooses ten different numbers and hopes that these get drawn. If the player's numbers get drawn, he/she wins an obscene amount of money. The table below displays the frequency with which classes of numbers are chosen (not drawn). These numbers came from a sample of 180 chosen numbers.
Chosen Numbers (n = 180)
| 1 to 10 | 11 to 20 | 21 to 30 | 31 to 40 | 41 to 50 | |
| Count | 42 | 54 | 27 | 34 | 23 |
The Test: Test the claim that all chosen numbers
are not evenly distributed across the five classes. Test this claim
at the 0.01 significance level.
(a) The table below is used to calculate the test statistic.
Complete the missing cells.
Round your answers to the same number of decimal places as
other entries for that column.
| Chosen | Observed | Assumed | Expected | ||||
| i | Numbers | Frequency (Oi) | Probability (pi) | Frequency Ei |
|
||
| 1 | 1 to 10 | 1 | 0.2 | 36.0 | 1.000 | ||
| 2 | 11 to 20 | 54 | 2 | 36.0 | 9.000 | ||
| 3 | 21 to 30 | 27 | 0.2 | 3 | 2.250 | ||
| 4 | 31 to 40 | 34 | 0.2 | 36.0 | 4 | ||
| 5 | 41 to 50 | 23 | 0.2 | 36.0 | 4.694 | ||
| Σ | n = 180 | χ2 = 5 | |||||
(b) What is the value for the degrees of freedom? 6
(c) What is the critical value of
χ2
? Use the answer found in the
χ2
-table or round to 3 decimal places.
tα = 7
(d) What is the conclusion regarding the null hypothesis?
reject H0 fail to reject H0
(e) Choose the appropriate concluding statement.
We have proven that all chosen numbers are evenly distributed across the five classes. The data supports the claim that all chosen numbers are not evenly distributed across the five classes. There is not enough data to support the claim that all chosen numbers are not evenly distributed across the five classes.
In: Math
A problem in a test given to small children asks them to match each of three pictures of animals to the word identifying that animal. If a child assigns the three words at random to the three pictures ,Find the probability distribution for Y , the number of correct matches.
In: Statistics and Probability
A group of four components is known to contain two defectives. An inspector tests the components one at a time until the two defectives are located. Let X denote the number of the test on which the second defective is found. Find the probability distribution for X.
In: Statistics and Probability
suppose that 25% of all licensed drivers in a particular state do not have insurance. let x be the number of uninsured drivers in a random sample of size 40. what is the probability that between 7 and 14 (both inclusive) of the selected drivers are uninsured?
In: Statistics and Probability
The number of imperfections in a particular type of wood has an average and variance of 1.5 imperfection in 10 cubic metres of the wood. Find the probability that a 10 cubic metre block of wood has at most one imperfection by hand and verify using MATLAB.
In: Statistics and Probability
There are 5 black balls and 9 red balls in an urn. If 4 balls are drawn without replacement, what is the probability that exactly 3 black balls are drawn? Express your answer as a fraction or a decimal number rounded to four decimal places.
In: Statistics and Probability
From a lot containing 25 items, 5 of which are defective, 4 are chosen at random. Let X be the number of defective items found. Obtain the probability distribution of X if (a) the items are chosen with replacement, (b) the items are chosen without replacement.
In: Statistics and Probability
There are 8 black balls and 6 red balls in an urn. If 4 balls are drawn without replacement, what is the probability that at least 3 black balls are drawn? Express your answer as a fraction or a decimal number rounded to four decimal places.
In: Statistics and Probability