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Mathematical expectation of continuous random variables
The integral result of 1 and (4x-m) is 2x? -mx |[2000→m]=2m? -m? -2*2000? +2000m

The integration result of 3m is 3mx |[m→4000]= 12000m-3m?

2、∫[-∞→+∞] yf(x) dx

=∫[-∞→2000]YF(x)dx+∫[2000→4000]YF(x)dx+∫[4000 →+∞]YF(x)dx

=∫[-∞→2000]0dx+∫[2000→4000](y/2000)dx+∫[4000 →+∞]0dx

=∫[2000→4000] (y/2000) dx

=∫[2000→m](y/2000)dx+∫[m→4000](y/2000)dx

=∫[2000→m](4x-m)/2000 dx+∫[m→4000](3m/2000)dx