Given a random variable X with expectation E[X] = 3 and variance V[X] = 3, calculate: E[(2+X)^2] V[4+3X]
Added by Martin A.
Step 1
So, E[2 + X] = 2 + E[X] = 2 + 3 = 5. Now, E[(2+X)^2] = E[(2+X)(2+X)] Expanding this, we get E[4 + 2X + 2X + X^2] = E[4 + 4X + X^2] Using the rule E[a + bX] = a + bE[X], we get E[4 + 4X + X^2] = 4 + 4E[X] + E[X^2] Substitute E[X] = 3, we get E[(2+X)^2] = 4 + 4(3) + Show more…
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