Verify that the total area under the density curve is indeed 1. 0.0 0.025x + 0.4 dx = (b) Calculate P(X ≤ 4). 2.3125 (c) Calculate P(3.5 ≤ x ≤ 4.5). Calculate P(4.5 < X). 5 How does this probability compare to P(X < 4)? OP(X ≤ 4) > P(X < 4) O P(X ≤ 4) = P(X < 4) O P(X ≤ 4) < P(X < 4) 3
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- The error, X, in measuring the length of a rivet (in micrometers) has the following probability density functionf(x)= 20·x·(3−x)3 243 for 0 ≤ x ≤ 3 and 0 otherwise.a) What is the probability that X > 1? b) What is the probability that X < 1? c) What is the probability that 2.1 < X < 2.7? d) What is the expected value of X (E(X))?Suppose the variables Q and W are skewed distributions defined over a limited set of values. What is the probability that W takes on a value between 0.5 and 1.75? What is E(W)? Suppose that the domain of W changes to 0<t<2.5, what happens to the Probability Density Function (PDF)?Suppose that a study of a certain computer system reveals that the response time, in seconds, has an exponential distribution with density curve f(x) = (1/3)e(-x/3) for x > 0 and f(x) = 0 otherwise. What is the probability that response time exceeds 5 seconds? What is the probability that response time exceeds 10 seconds?
- Let Y1 = 0.5, Y2 = 0.25, Y3 = 0.75, Y4 = 0.25 and Y5 = 1.25 be a random sample of width 5 selected from the population with the following probability density function. Which of the following is the estimation value obtained by the moment method for the unknown q parameter of this population?Suppose that the random variable B has the standard normal density. What is the conditional probability density function of the sum of the two roots of the quadratic equation x2 + 2Bx + 1 = 0 given that the two roots are real? KINDLY REQUEST YOU TO PROVIDE ME WITH COMPLETE SOLUTIONSuppose that the unknown X is ≥ 2 and has the probability density function fX(x)=Ce^−x,x ≥ 2.What is the numerical value of C?
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