2. X and Y are independent and identically distributed Rayleigh variables, each b = 5. What is the probability that (1) X>Y (2) X>2Y? Repeat by finding P(X >cY) where cis a positive integer.
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- show that if A occurs in a larger proportion of the cases where B is than wgere B is not, then B will occur in a larger proportion of cases where A is than where A is not.If the critical t is ±1.796 and the obtained t is -2.09, what decision would you make regarding the null hypothesis?For b there are two cases and for c I have to plug the initial data into the ode
- In testing the hypotheses H0: p = 0.5 vs Ha: p <= 0.5, suppose you get a p-value 0.022. Thenyou realize that the one sided alternative is too restrictive and re-do the test with a two sidedalternative Ha : p =/= 0.5.Based on the new p-value, what will be your conclusion ? A. Reject H0 at alpha = 0.01 but not at alpha = 0.05; 0.1.B. Reject H0 at alpha = 0.05 and alpha = 0.1 but not at alpha = 0.01.C. Fail to reject H0 at all the above alpha values.D. Reject H0 at alpha = 0.05 and alpha = 0.01 but not at alpha = 0.1.E. Reject H0 at all the above alpha values.Consider the linear model Yi = B0 + B1X1i + B2X2i + ui where ui is the error term and where E(ui|X1i,X2i) = 0, observations (Yi,X1i,X2i) are independent and identically distributed, 0 < E(Y4) < 1, 0 < 1i E(X14i) < 1, 0 < E(X24i) < 1 and where X2i = X12i. Are the OLS estimators Bˆ1 and Bˆ2 of the coe¢cients B1 and B2 unbiased and consistent? Explain.*A Consumer is willing to trade 3 unit of x for unit 1 of y ,when she has 6 unit of x and 5 unit of y.she also willing to trade in 6 unit of x for 2 unit of y,when she has 12 unit of x and 3 unit of y.she is indifferent between bundle (6,5) and bundle (12,3).what is the utility function of for goods x and y? hint: what is the shape of indifference curve?*
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