Match the degrees of freedom to its possible graph of the χ2 distribution. Not all choices are selected. Graph #1, #2, #3 (see attached)  Options (to select from):  50 300 10 3

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Match the degrees of freedom to its possible graph of the χ2 distribution. Not all choices are selected.

Graph #1, #2, #3 (see attached) 

Options (to select from): 

  • 50
  • 300
  • 10
  • 3
The image contains three graphs, each depicting a different probability distribution.

1. **Graph 1 (Top Graph): Normal Distribution**
   - This graph represents a normal distribution, also known as a Gaussian distribution, often referred to as a bell curve due to its shape.
   - The x-axis ranges from 0 to 90, with a peak around the middle (approximately 50), indicating the mean of the distribution.
   - The curve is symmetrical around the mean, and the tails approach the x-axis but never touch it.

2. **Graph 2 (Middle Graph): Log-Normal Distribution**
   - This graph displays a log-normal distribution.
   - The x-axis is marked with tick marks, and the curve is skewed to the right, indicating that this distribution is not symmetric.
   - The peak is located towards the left side, with a long tail extending to the right.
   - This distribution is often used in statistics to model variables that are positively skewed.

3. **Graph 3 (Bottom Graph): Gamma Distribution**
   - The final graph depicts a gamma distribution.
   - The x-axis ranges from 0 to 8, with values increasing to 0.3 on the y-axis.
   - The curve rises sharply to a peak at around 1, then gradually declines as it moves to the right, indicating a right-skewed distribution.
   - The gamma distribution is commonly used to model wait times and is characterized by its shape (α parameter) and scale (β parameter).

These graphs illustrate three different types of probability distributions, each with unique characteristics used to model various statistical phenomena.
Transcribed Image Text:The image contains three graphs, each depicting a different probability distribution. 1. **Graph 1 (Top Graph): Normal Distribution** - This graph represents a normal distribution, also known as a Gaussian distribution, often referred to as a bell curve due to its shape. - The x-axis ranges from 0 to 90, with a peak around the middle (approximately 50), indicating the mean of the distribution. - The curve is symmetrical around the mean, and the tails approach the x-axis but never touch it. 2. **Graph 2 (Middle Graph): Log-Normal Distribution** - This graph displays a log-normal distribution. - The x-axis is marked with tick marks, and the curve is skewed to the right, indicating that this distribution is not symmetric. - The peak is located towards the left side, with a long tail extending to the right. - This distribution is often used in statistics to model variables that are positively skewed. 3. **Graph 3 (Bottom Graph): Gamma Distribution** - The final graph depicts a gamma distribution. - The x-axis ranges from 0 to 8, with values increasing to 0.3 on the y-axis. - The curve rises sharply to a peak at around 1, then gradually declines as it moves to the right, indicating a right-skewed distribution. - The gamma distribution is commonly used to model wait times and is characterized by its shape (α parameter) and scale (β parameter). These graphs illustrate three different types of probability distributions, each with unique characteristics used to model various statistical phenomena.
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