Question
For $s<t$, argue that $B(s)-\frac{s}{t} B(t)$ and $B(t)$ are independent.
Step 1
Recall the definition of independent random variables: Two random variables X and Y are independent if the joint probability distribution of X and Y is the product of their marginal probability distributions, i.e., P(X = x, Y = y) = P(X = x)P(Y = y) for all x and Show more…
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'Exercise 3. Suppose that A and B are independent: Argue that A and B are also independent:'
Suppose that $A$ and $B$ are independent events. Show that $A^{c}$ and $B$ are also independent.
Show that if $A$ and $B$ are independent, then $A$ and $B^{c}$ as well as $A^{c}$ and $B^{c}$ are independent.
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