Mathematical Statistics and Data Analysis
3rd Edition
ISBN: 9781111793715
Author: John A. Rice
Publisher: Cengage Learning
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For a discrete random variable X if : Points ) P ( X = x ) = 0.1x , x = 2 , 3 , 5 , then E ( X2 ) =
Prove - If X and Y are independent random variables, then E(XY ) = E(X)E(Y ). (You can assume that both X and Y are either continuous or discrete random variables.)
Let X and Y are independent Poisson random variables such that E(X) = E(Y)=2. Let Z=X+Y. Compute P(X=2|Z=3).
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- Consumer Preference In a population of 100,000 consumers, there are 20,000 users of Brand A, 30,000 users of Brand B, and 50,000 who use neither brand. During any month, a Brand A user has a 20 probability of switching to Brand B and a 5 of not using either brand. A Brand B user has a 15 probability of switching to Brand A and a 10 probability of not using either brand. A nonuser has a 10 probability of purchasing Brand A and a 15 probability of purchasing Brand B. How many people will be in each group a in 1 month, b in 2 months, and c in 18 months?arrow_forwardAssume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.arrow_forwardLet X be a discrete random variable with support {0,2,3}, and suppose E(X) =1 and P(X=0)=P(X=2). Find Var(X)arrow_forward
- Suppose X is a discrete random variable and P(X = x) = (x+1)2 / C, for some positive constant C and for all x ∈ {0,1,3,4}. Solve for C and find the cdf of X.arrow_forwardLet X ~ U(a,b). Use the definition of the mean of a continuous random variable to show that μX = (a+b)/2.arrow_forwardLet (X1 ; X2) are jointly distributes random variables with discrete joint probability function p(X1 ; X2) = K(X1 + X2) where X1=0,1 and X2=0,1,2. Find the value of K Compute P((X1+X2) < 2) Compute P(X1=1 | X2=0) Compute E(X1X2)arrow_forward
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