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For each probability density function, over the given interval, find
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- Given the probability density function f (x)=1/2 over the interval [2,4] find the expected value, the mean, the variance and the standard deviation. Expected value: Mean: Variance: Standard Deviation:arrow_forwardA random variable X has the probability function as given in the table to the right. It is easy to show that the mean value is 5. Find the variance of X. X P(X) 3 0.2 5 0.6 7 0.2arrow_forwardThe Binomial random variable X has PMF P(X = x) = a. State the probability distribution table for the random variable X b. Find the expected value of X C. Find the variance of X d. Find the standard deviation of X e. Find P[ux – Ogarrow_forwardSuppose that the probability that a patient admitted in a hospital is diagnosed with a certain type of cancer is 0.04. Suppose that on a given day 10 patients are admitted and X denotes the number of patients diagnosed with this type of cancer. The mean and the variance of X are: O E(X)=0.4 and V(X)=0.384 O None of these O E(X)=0.5 and V(X)=0.475 E(X)=0.3 and V(X)=0.291arrow_forwardWhich of the following tables shows a valid probability density function? Select all correct answers. Select all that apply: x P(X=x) 0 0.6 1 0.01 2 0.14 x P(X=x) 0 310 1 110 2 25 x P(X=x) 0 18 1 14 2 58 x P(X=x) 0 0.13 1 0.09 2 0.45 3 0.27 4 0.06 x P(X=x) 0 −15 1 310 2 12 3 310 4 110 x P(X=x) 0 12 1 18 2 38arrow_forwardThe random variables A and B have variances 0.2 and 0.5 respectively. Let T= 5A+2B. The variance of T is 6 a. True b. False <arrow_forwardConsider the bivariate distribution for the random variables x and y. The correlation coefficient of x and y is the covariance a. Consider the bivariate distribution for the random variables x and y. The correlation coefficient of x and y is the covariance b. multiplied by the product of the standard deviations for x and y. c. multiplied by the standard deviation of y and divided by the standard deviation of x. d. multiplied by the standard deviation of x and divided by the standard deviation of y.arrow_forwardThe random variable X takes value O with probability, and value 1 with the remaining probability. The random variable Y takes value 100 with probability and value 101 with the remaining probability. What is the relation between the variance of X and the variance of Y? Var[X] Var[Y] "arrow_forwardPhone Battery Life. Battery life between charges for a certain mobile phone is 20 hours when the primary use is talk time and drops to 7 hours when the phone is primarily used for Internet applications over a cellular network. Assume that the battery life in both cases follows an exponential distribution. a. Show the probability density function for battery life for this phone when its primary use is talk time. b. What is the probability that the battery charge for a randomly selected phone will last no more than 15 hours when its primary use is talk time? c. What is the probability that the battery charge for a randomly selected phone will last more than 20 hours when its primary use is talk time? d. What is the probability that the battery charge for a randomly selected phone will last no more than 5 hours when its primary use is Internet applications?arrow_forwardNEED ASAP HELParrow_forwardSolve each problem on a separate sheet of paper. Show all necessary solutions. 1. Let X denotes the percentage of time out of a 40-hour workweek that a call center agent is directly serving a client by answering phone calls. Suppose that X has a probability density function defined by f(x) = 3r for 0 sxs 1. Find the mean and variance of X. Interpret the results. %3Darrow_forwardFind the variance and the standard deviation of Xarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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