Answer to Question #295774 in Statistics and Probability for jay

Question

1. How do you determine the probability of a random variable? 2. How do you construct the bar graph of a probability distribution?

Answer 1

Solution:

(1) The probability distribution for a discrete random variable X can be represented by a formula, a table, or a graph, which provides p(x) = P(X=x) for all x.

(2) Creating Probability Distribution Graphs

Creating the x values (horizontal axis)

1. Choose Calc / Make Patterned Data / Simple Set of Numbers
2. Store the patterned data in x
3. Enter the left hand value of the graph for the first value
4. Enter the right hand value of the graph for the last value
5. The step size depends on the type of distribution.
6. For a discrete distribution like the binomial that only has integer values, use 1.
7. For a continuous distribution like the normal, t, chi-square, or F, use a small value like 0.05 or 0.02. The smaller the value, the smoother the curve will be.
8. Click OK

Creating the y values (vertical axis)

1. Choose Calc / Probability Distributions and then select the name of the distribution you're wanting to graph. This can be normal, t, chi-square, or F.
2. Check the box for probabilty density. This is the height (y-value) of the curve. The cumulative probability tells you the area to the left of the x value and the inverse cumulative probability tells you the x-value when you know the area to the left of the value.
3. Enter any required parameters
4. Binomial: Enter the number of trials and probability of success on each trial (called event probability)
5. Normal: There are no required parameters that need changing. Leave the mean at 0 and standard deviation at 1.
6. T: Enter the degrees of freedom. Leave the non-centrality parameter at 0.
7. Chi-square: Enter the degrees of freedom. Leave the non-centrality parameter at 0.
8. F: Enter the numerator degrees of freedom and the denominator degrees of freedom. Leave the non-centrality parameter at 0.
9. The input column is x
10. The optional storage is p (for probability, although you could call it y if you like)
11. Click OK