pugh (d) below. bility distribution for the random variable x. laces as needed.) lity distribution. Choose the correct graph below.

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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The image presents data on smartphone game ratings, using a 1 to 5 star system, where 1 signifies a poor rating. 

### Ratings Data:
- **Stars: Frequency**
  - 1 Star: 2,255
  - 2 Stars: 2,497
  - 3 Stars: 5,000
  - 4 Stars: 3,673
  - 5 Stars: 11,267

### Tasks:

#### (a) Construct a Discrete Probability Distribution
Develop a probability distribution for the random variable representing the stars (\( x \)) using the given frequencies. Compute probabilities \( P(x) \) as follows:

\[ P(x) = \frac{\text{Frequency of } x}{\text{Total Frequency}} \]

**Example**: Total Frequency = 2,255 + 2,497 + 5,000 + 3,673 + 11,267

Fill in the probability \( P(x) \) for each star rating, rounding to three decimal places if necessary.

#### (b) Graph the Discrete Probability Distribution
Illustrate the probability distribution using a suitable graph. The graph will have:
- X-axis: Star Ratings (1 to 5)
- Y-axis: Corresponding Probabilities \( P(x) \)

This exercise requires calculating the probabilities and visually representing the distribution to understand the rating trends of the smartphone game.
Transcribed Image Text:The image presents data on smartphone game ratings, using a 1 to 5 star system, where 1 signifies a poor rating. ### Ratings Data: - **Stars: Frequency** - 1 Star: 2,255 - 2 Stars: 2,497 - 3 Stars: 5,000 - 4 Stars: 3,673 - 5 Stars: 11,267 ### Tasks: #### (a) Construct a Discrete Probability Distribution Develop a probability distribution for the random variable representing the stars (\( x \)) using the given frequencies. Compute probabilities \( P(x) \) as follows: \[ P(x) = \frac{\text{Frequency of } x}{\text{Total Frequency}} \] **Example**: Total Frequency = 2,255 + 2,497 + 5,000 + 3,673 + 11,267 Fill in the probability \( P(x) \) for each star rating, rounding to three decimal places if necessary. #### (b) Graph the Discrete Probability Distribution Illustrate the probability distribution using a suitable graph. The graph will have: - X-axis: Star Ratings (1 to 5) - Y-axis: Corresponding Probabilities \( P(x) \) This exercise requires calculating the probabilities and visually representing the distribution to understand the rating trends of the smartphone game.
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