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For Exercises 15–20, (a) find the median of the random variable with the probability density function given, and (b) find the probability that the random variable is between the expected value (mean) and the median. The expected value for each of these functions was found in Exercises 1–8.
18.
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Finite Mathematics and Calculus with Applications
- Part B 1) The probability density function is f(x) = 2e-kx i) Standard deviation of x = ?.arrow_forwardIn the transmission of digital information, the probability that a bit has high, moderate, and low distortion is 0.01, 0.04, and 0.95, respectively. Suppose that three bits are transmitted and that the amount of distortion of each bit is assumed to be independent. Let X and Y denote the number of bits with high and moderate distortion out of the three, respectively. Determine: E(x) =arrow_forwardQ.2 Let X has the following probability density function: fx(x) = a e-ax;x > 0 Find moment generating function and then using it find mean and variance. End of Quizarrow_forward
- TF.8arrow_forwardEstimate the probability that a missile fired at speed x = 350 knots will hit the target.arrow_forwardConsider the function: f(x)= −1 − x^2 Which of the following is true? A. This function is a pdf only for some values of random variable B. This function cannot be a pdf for any set of values of random variable C. None of these D. This function is a pdf for any set of values of random variable.arrow_forward
- In information theory (the mathematical study of communication systems, which figures prominently in electrical engineering), the information (or entropy) of a discrete and finite random variable X is defined as: H(X)= E[log2(1/P(X))] where p(.) is the PMF for X. Answer the following: 1. Assume that the set of values that X can take is {x1, ..., xn} and p(x;) > 0 for all i. Derive an expression for H(X) in terms of p(x1), ..., p(xn). 2. Assume that n = 2. What values of p(x1) and p(x2) maximize H(X)?arrow_forwardExample 2: Consider the following function shown below, Use it to answer the following questions. x3 P(x) = 9' x = 0,1,2 a) Determine whether or not the function shown above is a valid probability function. b) Construct a probability histogram for the function shown above and comment on the shape. domye c) Find P(x > 1)arrow_forwardMany professional baseball teams (including the Cincinnati Reds and the Boston Red Sox) use Bill James's formula to estimate their probability of winning a league pennant: (Runs scored)2 (Runs scored)2 + (Runs allowed)2 Probability) of winning This formula, whose form is reminiscent of the Pythagorean theorem, is considered more accurate than just the proportion of games won because it takes into consideration the scores of the games.t Find this probability for a team that has scored 500 runs and allowed 400 runs. (Round your answer to the nearest whole percent.)arrow_forward
- (Sec. 3.2) A student is required to enroll in one, two, three, four, five, six on the desired courseload) at a local university. Let Y the number of classes the next student enrolls themselves in. The probability that y classes are selected is known to be proportional to y+1, in other words the pmf of Y is given by p(y) = k(y+1) for y 1,...,7, and 0 otherwise (a) What is the value of k? or seven classes (depending (b) What is the probability that at most four classes are enrolled in? (c) What is the probability that a student enrolls in between three and five classes (inclusive)? y? /40 for y 1,.,7 be the pmf of Y? Explain why why not (d) Could p(y) orarrow_forwardTABLE 3: Number of packs with X number of RED candy x (Red Candy) 7 8 9 10 11 Total f (Pack) 3 5 3 3 1 15 Based on Table 3, find the probability that the number of red candy is: Less than the mean of X More than or equal to the mean of X Between and (E (X) - 1) and (E (X) + 1)arrow_forwardQuestion C.26arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill