2. A company may makes infant, toddler, or child toys and the sales will be effected by which of three cartoons get the highest ratings. Show A has a 0.3 probability or getting the highest rating, Show B has 0.4, and Show C has 0.3. They payoffs are in the table below. Show A Show B Show C Infant 7 -2 6. Toddler -3 8. -1 Child 2 -4 8
2. A company may makes infant, toddler, or child toys and the sales will be effected by which of three cartoons get the highest ratings. Show A has a 0.3 probability or getting the highest rating, Show B has 0.4, and Show C has 0.3. They payoffs are in the table below. Show A Show B Show C Infant 7 -2 6. Toddler -3 8. -1 Child 2 -4 8
MATLAB: An Introduction with Applications
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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![### Problem Statement
A company that manufactures toys for infants, toddlers, and children wants to evaluate how the sales of their products will be affected by the ratings of three different TV shows. Each show has a specific probability of receiving the highest rating, and the impact of each show on toy sales is given in a payoff matrix.
### Probabilities of Getting the Highest Rating
- **Show A**: 0.3 probability
- **Show B**: 0.4 probability
- **Show C**: 0.3 probability
### Payoff Matrix
The table below illustrates the potential sales impact (payoffs) for each type of toy (infant, toddler, and child) based on which TV show receives the highest rating.
| | Show A | Show B | Show C |
|--------|--------|--------|--------|
| Infant | 7 | -2 | 6 |
| Toddler| -3 | 8 | -1 |
| Child | 2 | -4 | 8 |
### Explanation of the Payoff Matrix
- **Infant Toys**
- Show A: Sales impact of 7
- Show B: Sales impact of -2
- Show C: Sales impact of 6
- **Toddler Toys**
- Show A: Sales impact of -3
- Show B: Sales impact of 8
- Show C: Sales impact of -1
- **Child Toys**
- Show A: Sales impact of 2
- Show B: Sales impact of -4
- Show C: Sales impact of 8
This payoff matrix can be used to determine the expected impact on toy sales by calculating the weighted average based on the probabilities of each show receiving the highest rating. This type of analysis can aid the company in strategic decision-making regarding which product lines to focus on or market more extensively based on television show ratings.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa0073c4-6425-40d1-a8ed-c26ddcc2ccc0%2Fdf77b822-a677-474e-aea5-3c085cac019a%2Fs9uwi3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
A company that manufactures toys for infants, toddlers, and children wants to evaluate how the sales of their products will be affected by the ratings of three different TV shows. Each show has a specific probability of receiving the highest rating, and the impact of each show on toy sales is given in a payoff matrix.
### Probabilities of Getting the Highest Rating
- **Show A**: 0.3 probability
- **Show B**: 0.4 probability
- **Show C**: 0.3 probability
### Payoff Matrix
The table below illustrates the potential sales impact (payoffs) for each type of toy (infant, toddler, and child) based on which TV show receives the highest rating.
| | Show A | Show B | Show C |
|--------|--------|--------|--------|
| Infant | 7 | -2 | 6 |
| Toddler| -3 | 8 | -1 |
| Child | 2 | -4 | 8 |
### Explanation of the Payoff Matrix
- **Infant Toys**
- Show A: Sales impact of 7
- Show B: Sales impact of -2
- Show C: Sales impact of 6
- **Toddler Toys**
- Show A: Sales impact of -3
- Show B: Sales impact of 8
- Show C: Sales impact of -1
- **Child Toys**
- Show A: Sales impact of 2
- Show B: Sales impact of -4
- Show C: Sales impact of 8
This payoff matrix can be used to determine the expected impact on toy sales by calculating the weighted average based on the probabilities of each show receiving the highest rating. This type of analysis can aid the company in strategic decision-making regarding which product lines to focus on or market more extensively based on television show ratings.
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