two random variables, A and B, are related by the equation B = 2A + 1. Suppose μA = 1 and σB = 2. What is the quantity μB + σA? (find μB and σA first)
two random variables, A and B, are related by the equation B = 2A + 1....
Two types of medication for hives are being tested to determine if there is a difference in the proportions of adult patient reactions. Twenty out of a random sample of 200 adults given medication A still had hives 30 minutes after taking the medication. Twelve out of another random sample of 180 adults given medication B still had hives 30 minutes after taking the medication. Test at a 1% level of significance. 1. The null and alternative hypothesis would be:...
Let X and Y be two independent and identically distributed random variables with expected value 1 and variance 2.56. First, find a non-trivial upper bound for P(|X + Y − 2| ≥ 1). Now suppose that X and Y are independent and identically distributed N(1,2.56) random variables. What is P(|X + Y − 2| ≥ 1) exactly? Why is the upper bound first obtained so different from the exact probability obtained?
Suppose X~Pois(A) and Y ~Pois(2A) are independent random variables. Consider a linear estimator of λ, that is, λ = aX + bY. (a) Find an expression for the bias of λ, in terms of a and b, and determine a condition on the values of a and b, such that λ is unbiased. (b) Of all the values of a and b that make the estimator unbiased, find the values of oa and b that minimize the variance of the...
Suppose random variables X and Y are related as Y=7X+3. Suppose the random variable X has mean 1, and variance 1. What is the expected value of X+Y ? Solution provided is 11. How was this obtained?
Consider the experimental results for the following randomized block design. Make the calculations necessary to set up the analysis of variance table. Treatments A B C Blocks 1 10 9 8 2 12 6 5 3 18 16 14 4 20 18 18 5 8 7 8 Use α = 0.05 to test for any significant differences. State the null and alternative hypotheses. H0: μA ≠ μB ≠ μC Ha: μA = μB = μCH0: μA = μB = μC...
Consider the experimental results for the following randomized block design. Make the calculations necessary to set up the analysis of variance table. Treatments A B C Blocks 1 10 9 8 2 12 6 5 3 18 15 14 4 20 18 18 5 8 7 9 Use α = 0.05 to test for any significant differences. State the null and alternative hypotheses. H0: μA = μB = μC Ha: Not all the population means are equal. H0: μA =...
The variables x and y are implicitly related to the equation x^4+ { ^Y down 1 e^-t^2 dt =1 ( Y is at the top of the { and 1 is at the bottom of the { ) The point p=(1,1) lies on the graph of the equation. Find the slope of the line tangent to the graph at the point p=(1,1) A.) 2e^-2 B.) 2e C.) -4e D.) -4e^-1 E.) 4e^-2
Suppose the random variables X, Y and Z are related through the model Y = 2 + 2X + Z, where Z has mean 0 and variance σ2 Z = 16 and X has variance σ2 X = 9. Assume X and Z are independent, the find the covariance of X and Y and that of Y and Z. Hint: write Cov(X, Y ) = Cov(X, 2+2X+Z) and use the propositions of covariance from slides of Chapter 4. Suppose the...
9. Let X and Y be two random variables. Suppose that σ = 4, and σ -9. If we know that the two random variables Z-2X?Y and W = X + Y are independent, find Cov(X, Y) and ρ(X,Y). 10. Let X and Y be bivariate normal random variables with parameters μェー0, σ, 1,Hy- 1, ơv = 2, and ρ = _ .5. Find P(X + 2Y < 3) . Find Cov(X-Y, X + 2Y) 11. Let X and Y...
[1] The joint probability mass function of two discrete random variables A and B is Pab(a,b) = {ca2b, a = -2,2 and b = 1,2 otherwise Clearly stating your reasons, answer the following two (1) Are A and B are uncorrelated? (ii) Are A and B independent? [2] X is continuous uniform (1,7) while Y is exponential with mean 2. If the variance of (X+2Y) is 20, find the correlation coefficient of X and Y.