Question 1177122
I'll find the value of c, the probability of a specific inflation rate outcome, and the cumulative distribution function (CDF).
```python?code_reference&code_event_index=3
from sympy import integrate, Symbol, oo

# Define the variable
x = Symbol('x')

# a) Find the value of c
c = 1 / integrate(x**-3, (x, 3, oo))
print(f"a) The value of c is: {c}")

# b) Find the probability that the inflation rate is greater than 20
p = integrate(c * x**-3, (x, 20, oo))
print(f"b) The probability that the inflation rate is greater than 20 is: {p}")

# Calculate the probability that exactly one out of five years has an inflation rate greater than 20
n = 5
k = 1
prob_1_out_of_5 = (p ** k) * ((1 - p) ** (n - k)) * (5 / 1)  # binomial probability formula
print(f"The probability that exactly one out of five years has an inflation rate greater than 20 is: {prob_1_out_of_5}")

# c) Find the cumulative distribution function (CDF)
cdf = integrate(c * x**-3, (x, 3, x))
print(f"c) The cumulative distribution function (CDF) is: {cdf}")
```
```text?code_stdout&code_event_index=3
a) The value of c is: 18
b) The probability that the inflation rate is greater than 20 is: 9/400
The probability that exactly one out of five years has an inflation rate greater than 20 is: 0.102711621801270
c) The cumulative distribution function (CDF) is: 1 - 9/x**2

```
Here are the results:

* **a) Value of c:**
   The constant c in the probability density function is 18.

* **b) Probability of exactly one year out of five with inflation greater than 20:**
   The probability that exactly one out of the next five years will have an inflation rate greater than 20 is approximately 0.1027.

* **c) Cumulative Distribution Function (CDF):**
   The cumulative distribution function (CDF) for the inflation rate (x) is:

   CDF(x) = 0, for x ≤ 3
   CDF(x) = 1 - 9/x^2, for x > 3

Let me know if you have any further questions or need more assistance with this or another problem!