The CDF of a random variable X is X < -1 (x + 1)/2 -1< x<1 x 2 1 Fx (x) = 1 a. What is P[X > 1/2]? b. What is P[-1/2 < X < 3/4]? c. What is P[|X|< 1/2]? d. What is the value of a such that P[X < a] = 0.8? Ans. A) 0.25 B) 0.625 C) 0.5 D) 0.6
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- Let the probability function of the random variable X bef(x) = { x/45 if x = 1, 2, 3, ⋯ ⋯ ,9 { 0 otherwiseFind E(X) and Var(X)A box consists of 12 components, 5 of which are defective. (a) Components are selected and tested one at a time, without replacement, until a non-defective component is found. Let X be the number of tests required. Find P(X = 6). (b) Components are selected and tested, one at a time without replacement, until two consecutive non defective components are obtained. Let X be the number of tests required. Find P(X = 5).You study a population and are interested in the proportionpthat has a certain characteristic. You are unaware that this proportion of the population isp=0.67. You have taken a random sample of sizen & 129of the population and determined that the proportion of the sample having the characteristic isp=0.73. His sample is Sample 1 in the following table. (In the table, Sample 1 is indicated by "M1", Sample 2 by "M2", and so on). (to) Based on Sample 1, plot the confidence intervals of80%and of95%for the population proportion. Use1,282for the critical value for the confidence interval of80%, and use1960 for the critical value for the confidence interval of95%. (If necessary, you can refer to a list of formulas.) • Write the upper limit and the lower limit on the graphs to indicate each confidence interval. Write the answers with two decimal places. • For the points ( ♦and ◆), write the population proportion,0.67. 0.47 0.47 80% confidence interval 0.65 X 0.84 0.84 0.47 0.47 95% confidence…
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- What is the decision rule for this test? Select one: a. Reject Ho if (n-1) s/%o > x-1, or x-1,a c. Reject Ho if (n-1) s²/o > x²-1.x d. Reject Ho if (n-1) s/%o >x-1,1-There are 2 players in a game. Each player independently picks a real number on the interval [0, 1] uniformly. If the (absolute) difference between the two numbers is less than a (0 < a < 1) and the sum of the two numbers is less than 1, then both players win, otherwise both players lose. What is the probability of winning? 2.Let X = b(n, and E(3x) = E(3-5x) find n.