Prob & Stats - Random Variable & Prob Distribution (26 of 53) Expected Value - Example 2

In this video I will find the expected value of the premium for a home insurance company with 1,000,000 policies with an average home price of $200,000.

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[ahmedal-ebrashy]

I think 200, 000-6 should be subtracted from one million. Either way thank you for teaching us many nice things :)

[srabonchowdhury]

Why is it (1, 000, 000/1, 000, 000)X and not {(1, 000, 000 - 2006)/1, 000, 000}X? I mean, why did we count every 1M policies? Why not subtracted the loss?

[joeyquiet]

small piece of python code to do the work :)
M1 = 1_000_000
P = np.array([6/M1, 2000/M1, M1/M1]).astype(np.float32)
X = np.array([-200_000, -3000, 0]).astype(np.float32)

index = 2
A=X
B=P
A_1 = np.concatenate([A[:index], A[index+1:]]) # A_1 is A without value at index
B_1 = np.concatenate([B[:index], B[index+1:]])
dotAB_1 = np.dot(A_1, B_1)
x = (-dotAB_1)/B[index]
print(f'insurance company should charge {x} to break even')