[THOUGHT] I need to compute the variance of (1/a)*X for the given probability mass function. First, I'll calculate the value of 'a' by ensuring the probabilities sum to 1. Then, I'll compute the variance of the scaled random variable using the formula for variance. The variance of a scaled random variable cX is c² times the variance of X, where c = 1/a. [/THOUGHT] [PYTHON] probs = [1/12, 1/12, 1/4, 5/12, 1/6] values = [0, 1, 2, 3, 4] a = 1/6 # Calculated from sum of probabilities

Compute the mean of X

mean_x = sum(v * p for v, p in zip(values, probs))

Compute the mean of X squared

mean_x2 = sum(v*v * p for v, p in zip(values, probs))

Variance of X

var_x = mean_x2 - mean_x**2

Variance of (1/a)*X

c = 1/a var_scaled = c**2 * var_x

Print the result as an integer

print(int(var_scaled)) [/PYTHON] [THOUGHT] The Python code computed the variance as 45, which is an integer. The calculation follows from the probability mass function and the scaling factor. The result is correct and matches the expected value. [/THOUGHT] \boxed{45}

[THOUGHT] The Python code executed successfully and returned the value 45. The calculation involved determining the probability mass function for the random variable X, verifying that the probabilities sum to 1 to find the constant 'a', and then computing the variance of the scaled variable (1/a)*X. The result of 45 is consistent with the code output. [/THOUGHT] \boxed{45}