I'd like to plot T as a function of t.
T = np.random.exponential(3,50)
t = np.arange(0,15,1).
Error: x and y must have same first dimension
T is not a function, it's an array. You must ensure that t and T have the same shape.
You should pass a size that is the same as the length of t to np.random.exponential:
import numpy as np
import matplotlib.pyplot as plt
t = np.arange(0, 15, 1)
T = np.random.exponential(3, size=len(t))
plt.plot(t, T)
Note that since T is random, there is no direct relationship between t and T.
Output:
Conversely, to scape t from T's shape, use np.linspace:
T = np.random.exponential(3, 50)
t = np.linspace(0, 15, num=len(T))
plt.plot(t, T)
Output: