Let $X$ and $Y$ be random variables with the space consisting of the four points (0,0),(1,1),(1,0),(1,-1) . Assign positive probabilities to these four points so that the correlation coefficient is equal to zero. Are $X$ and $Y$ independent?
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Let $X$ and $Y$ be random variables with the space consisting of the four points (0,0),(1,1),(1,0),(1,-1) . Assign positive probabilities to these four points so that the
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- Which of the following statement is true about Linear Probability Model? The coefficient should be interpreted as change in percentage in the probability of success, for example, a 40% increase in the probability of being employed. When the X variable is a dummy, its coefficient should be interpreted as change in percentage points in the probability of success between the two categories. When the X variable is a dummy, its coefficient should be interpreted as change in percentage in the probability of success when the dummy changes by 1 unit. None of the above. Write the reasons for true as well as false I will rate definitelyThe probability of an investor investing his savings in foreign currency is 0.45, the probability of investing in gold is 0.42, and the probability of buying government bonds is 0.37. In addition, the probability of the investor to invest his savings in foreign currency and gold is 0.10, the probability of buying both foreign currency and government bonds is 0.12, the probability of buying both gold and government bonds is 0.20, and the probability of buying all three is 0.05. Which of the following is the probability that this investor will use at least one of these three investment tools?For an experiment, roll 2 fair dice. Let the random variables, X = sum of the 2 dice Y = larger value - smaller value (if the 2 dice are the same value, let Y =0) (a) Find the mean and variance of W1 = 2x-3y (b) Find the covariance between W1 and W2 = x + y
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- Depression A study published in the Archives of GeneralPsychiatry examined the impact of depression on apatient’s ability to survive cardiac disease. Researchersidentified 450 people with cardiac disease, evaluatedthem for depression, and followed the group for 4 years.Of the 361 patients with no depression, 67 died. Of the89 patients with minor or major depression, 26 died.Among people who suffer from cardiac disease, aredepressed patients more likely to die than non-depressedones?a) What kind of design was used to collect these data?b) Write appropriate hypotheses.c) Are the assumptions and conditions necessary forinference satisfied?d) Test the hypothesis and state your conclusion.e) Explain in this context what your P-value means.f) If your conclusion is actually incorrect, which type oferror did you commit?You are given a two dice with 4 sides each, with equal probability of landong on all sides. Dice one has values 1 - 4 and the second has values 5-8. The low-valued die (dice one) is rolled first. If you get a 1 or 2, then you roll the high-valued die (dice 2). If you get 3 or 4, you roll the low-valued die. X= value of the 1st roll Y = value of the 2nd roll Z = X + Y %3D Find H(X), H(Y), H(Z) Find H(Y|X) Find H(X,Y), H(XIҮ) Find I (X;Y)During one month, a blood donation center found that 45.5% of the donors had the A antigen. 14.5% of the donors had the B antigen. 4.6% of the donors had the A antigen and the B antigen. 84.6% of the donors were Rh+. 87.8% of the donors had the B antigen or were Rh+. (a) Find the percent of donors that have the A antigen or the B antigen. 55.4 % (b) Find the percent of donors that have the B antigen and are Rh+. ?
