Suppose the current exchange rate from Canadian dollars (CAD) to US dollars (USD

Question

Suppose the current exchange rate from Canadian dollars (CAD) to US dollars (USD) is 0.71338 (that is, 1 CAD = 0.71338 USD). A friend of yours frequently crosses into the United States and carries a certian amount of money (in CAD) with him. The amount of money (in CAD) he carries into the US can be expressed as a random variable XX with E(X)E(X) = $91.25 and VAR(X)VAR(X) = $10.49.

Round all following answers to 2 decimals.?

b. Suppose that, before entering the US, he meets a relative who always gives him half what he started with so that he has a bit of extra money for his trip. After he is given this extra money, what is the standard deviation of the amount of money he has after exchanging it to USD? $?

Explanation / Answer

Here, X : amount of money he carries into the US. Also, E(X) = 91.25 and Var(X) = 10.49.

Now, his relative gives him the extra amount. Then, Y : amount of money he carries into the US after receiving the extra amount.

Here, Y = X + (1/2 * X) = 3/2 X.
Now, Var(Y) = 9/4 * Var(X) = (9/4) * 10.49 = 23.6025.

Now, standard deviation = square root of 23.6025 = $4.86

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