The sample space of a random experiment is the set of positive real numbers, S={x|x>0}. Define events A and B as A={x | x > 40} and B= {x|x < 65). Describe each of the following events: a) B' = b) ANB
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- A QR code photographed in poor lighting, so that it can be difficult to distinguish black and white pixels. The gray color (X) in each pixel is therefore coded on a scale from 0 (white) to 100 (black). The true pixel value (without shadow) the code is Y = 0 for white, and Y = 1 for black. We treat X and Y as random variables. For the highlighted pixel in the figure is the gray color X = 20 and the true pixel value is white, i.e. Y = 0. We assume that QR codes are designed so that, on average, there are as many white as black pixels, which means that pY (0) = pY (1) = 1/2. In this situation, X is continuously distributed (0 ≤ X ≤ 100) and Y is discretely distributed, but we can still think about the simultaneous distribution of X and Y. We start by defining the conditional density of X, given the value of Y : fX|Y(x|0) = "Pixel is really white" fX|Y(x|1) =" Pixel is really balck " Use Bayes formula as given in the picture and find the probability for x = 20 like in the picture.Cards are picked sequentially without replacement from a well-shuffled deck of 52 cards until either all SPADES are found or all CLUBS are found. Let X denote the number of cards picked. Find E(X) using indicator random variables.36) The time X needed to complete a final examination in a particular College Course is normally distributed with a mean of 60 minutes and standard deviatation of 10 minutes. The Probability of completing The exam in less than 70 minutes. is A) 0.9655. B)0, 1387 C) 0.8413 D) 0.0345
- A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X = the number among the n test results that are positive (indicating presence of the disease, so X is the number of false positives) and p = the probability that a disease-free individual's test result is positive (i.e., p is the true proportion of test results from disease-free individuals that are positive). Assume that only Xi available rather than the actual sequence of test results. (a) Derive the maximum likelihood estimator of p. p = If n = 20 and x = 7, what is the estimate? p = (b) Is the estimator of part (a) unbiased? Yes No (c) If n = 20 and x = 7, what is the mle of the probability (1 − p)5 that none of the next five tests done on disease-free individuals are positive? (Round your answer to four decimal places.)2. Let X, X,.., x, be a random sample from a distribution with p.d.f. f(x;0)=0x, |>x>0 Is the MLE O EE of 0? AEE of 0?Determine the distribution of the random variable X and sketch its graph. for a E (-00, -1) x € [-1, }) for e € [},2) 品 for for a) F(x) = x € [2, ) æ € },+) 17 20 for too) 1
- Suppose the random variable X follows a normal distribution with mean 80 and variance 100. Then the probability is 0.6826 that X is in the symmetric interval about the mean between two numbers are A) -2 to 2 B) -3 to 3 C) -1 to 1 D) noneThe sample space of a random experiment is the set of positive real numbers, $={x 1 x >0} Define events A and B as A={x | x > 40} and B={x | x < 65). Describe each of the following events: a) A' b) AUBAssume that the height, X, of a college woman is a normally distributed random variable with a mean of 65 inches and a standard deviation of 3 inches. Suppose that we sample the heights of 180 randomly chosen college women. Let M be the sample mean of the 180 height measurements. Let S be the sum of the 180 height measurements. All measurements are in inches. Using R and write the code out.a) What is the probability that X < 59? b) What is the probability that X > 59? c) What is the probability that all of the 180 measurements are greater than 59? d) What is the expected value of S? e) What is the standard deviation of S? f) What is the probability that S-180*65 >10? g) What is the standard deviation of S-180*65 h) What is the expected value of M? i) What is the standard deviation of M? j) What is the probability that M >65.41? k) What is the standard deviation of 180*M? l) If the probability of X > k is equal to .3, then what is k?
- Please help with this statistics problem. A traffic light at a certain intersection is green 45% of the time, yellow 10% of the time, and red 45% of the time. A car approaches this intersection once each day. Let X represent the number of days that pass up to and including the first time the car encounters a red light. Assume that each day represents an independent trial. A.) Find P(X=3). B.) Find P(X<=3) C.) Find ux. D.) Find 02/x.The length, X, of a lionfish is a normally distributed random variable with a mean of 13.5 inches and a standard deviation of 2.4 inches. Suppose that we measure the lengths of 150 randomly chosen lionfish. Let M be the sample mean of the 150-length measurements. Let S be the sum of the 150 length measurements.a) What is the probability that X < 9.3? b) What is the probability that X > 9.3? c) What is the probability that all of the 150 measurements are greater than 9.3? d) What is the expected value of S? e) What is the standard deviation of S? f) What is the probability that S-150*13.5 >10? g) What is the standard deviation of S-150*13.5 h) What is the expected value of M? i) What is the standard deviation of M? j) What is the probability that M >13.6? k) What is the standard deviation of 30*M? l) If the probability of X > k is equal to .8, then what is k?A sample space has 3 outcomes, {O1, O2, O3}. Suppose E= {O1, O2}, and F= {O1, O3}. If Pr[E]= 0.67 and Pr[F]= 0.54, what is Pr[{O2, O3}]?
