Let's say we have a biased coin that lands on heads with a 3/4 probability and...

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Let's say we have a biased coin that lands on heads with a 3/4 probability and tails with a 1/4 probability. In a series of independent coin tosses, we will denote Xi as 1 when the ith toss results in heads, and 0 when it does not. (a) Compute E[X₁] and var[X₁]. (b) Compute Var[X₁ + 2X₂ + 3X3 + 4X4]. Let's say we have a biased coin that lands on heads with a 3/4 probability and tails with a 1/4 probability. In a series of independent coin tosses, we will denote Xi as 1 when the ith toss results in heads, and 0 when it does not. (a) Compute E[X₁] and var[X₁]. (b) Compute Var[X₁ + 2X₂ + 3X3 + 4X4].

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a To compute the expected value EX1 and variance varX1 of X1 we can use the formulas for the mean an... View the full answer