A random variable X takes values between 4 and 6 with a probability density function f (x) = xln(1.5) for 4
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- What is the expected value of a continuous probability distribution given by the density function f(x) = 2x for 0 < x < 1?A random variable X has cumulative distribution functionA random variable X has a probability density function 0; x<0, f(x) = 0≤x≤ 1, ; 1a continuous random variable with probability density function given v f(x): de-/100 0. What is the probability that • (a) a computer will function between 50 and 150 hours before breaking down? (b) it will function for fewer than 100 hours?The probability density function for a continuous random variable X is given by 0 < x < 1 1≤ x ≤ 2 else Find P(0.5 < X < 1.5) Round to 4 decimal places if needed. f(x) = X 2-xThe service life T (this year) of a particular type of electric toothbrush is assumed to have the probability density f given by: see figure question (a) Find the probability that a randomly selected toothbrush (of this type) has a lifespan of more than 2 years.(b) Assume that a toothbrush of the same type has been working for one year already. What is the probability that it works for at least another 3 years?(c) What is the probability that the average lifespan of T¯ for 90 independent toothbrushes is greater than 2.1 years?Determine the probability density function of the random variable X* if x 1 ON|30The total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year is a random variable X having the density function shown to the right. Find the variance of X (x-8). f(x)2-(X-8). 9sx< 10, 8Let X be a random variable that follows the beta distribution. This random variable is continuous and is defined over the interval from 0 to 1. The probability density function is given by whereand are integers, whose values determine the shape of the probability density function. Because X varies between 0 and 1, we can think of X as the probability that some event (say) E occurs or the proportion of times an event occurs in some population. For example, E could denote the event that a critical part in a newly designed car will lead to a catastrophic failure in accidents at high speeds. The expected value (i.e., mean) of this random variable is []. That is, . The Excel commands for the beta random variable are =beta.dist(x,,,true,0,1) for the cumulative probability distribution, and =beta.dist(x,,,false,0,1) for the probability density function. (a) Now, think in Bayesian terms.…The probability density function of the time it takes a hematology cell counter to complete a test on a blood sample is f(x) = 0.04 for 58 < x< 83 seconds. Round your answers to 2 decimal places. (a) What proportion of tests require more than 70 seconds to complete? i (b) What proportion of tests require less than one minute to complete? i (c) Determine the mean and variance of the time to complete a test on a sample. Mean = i seconds Variance = i seconds?The proportion of people who respond to a certain mail-order solicitation is a continuous random variable X that has the density function (2x + 4 0 < x<1 f(x) = - 0, 5 elswhere Find the stàndard deviation of above stated continuous random variable (X)Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON