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f Y is a discrete random variable with expected value E[Y ] = µ and if X = a + bY , prove that Var (X) = b2Var (Y ) .
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Financial institutions often create synthetic instruments out of existing instruments. In this case an investment bank plans to buy Treasury Bonds with 20-year maturities at their
A survey was done where a random sample of people 18 and over were asked if they preferred comedies, dramas, or neither. The information gathered was broken down by age group and t
Decision Theory Decisions There are many types of decision making 1. Decision making under uncertainty It refer to situations where more than one outcome can r
Tommy has a Nexus 4 that charges poorly. He placed his phone to charge,after 20 minutes the phone was 27% and after 85 minutes the phone was at 66%. Find how many percentage the p
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The ratio of the sum of first n terms of two AP's is 7n+1:4n+27. Find the ratio of their 11th terms . Ans: Let a 1 , a 2 ... and d 1 , d 2 be the I terms are Cd's of t
The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(
Chain Rule : Assume that we have two functions f(x) & g(x) and they both are differentiable. 1. If we define F ( x ) = ( f o g ) ( x ) then the derivative of F(x) is,
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