b) The discrete random variable X has the probability distribution: x P(X = x) 2 c 4 2c 6 3c 8 4c i. Show that c = 0.1 [3 Marks] ii. Find E(X) [3 Marks] iii. Find E($$X^2$$) [3 Marks] iv. Find VAR(3 - 4X) [3 Marks]
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So, we have: $$P(X=2) + P(X=4) + P(X=6) + P(X=8) = 1$$ $$c + 2c + 3c + 4c = 1$$ Step 2: Combine the terms with 'c': $$(1+2+3+4)c = 1$$ $$10c = 1$$ Step 3: Solve for 'c': $$c = \frac{1}{10}$$ $$c = 0.1$$ This shows that c = 0.1. Step 4: To find E(X), the expected Show more…
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