The loss due to a fire in a commercial building is modeled by a random variable X with density function f(x) = 0.005(20 – x), 0 < x < 20. Given that a fire loss exceeds 8, what is the probability that it exceeds 16?

The density function of the continuous random variable X is shown below. When c≈ 0.163, Find: (1) the mode, (2) the median, and (3) the mean. Jcsin (2 -0.2x) for 1≤ x ≤ 10 f(x) = {0 elsewhere mahamdy@uoanbar.edu.iq

For a laboratory assignment, if the equipment is working, the density function of the observed outcome X is f(x) = 2x(1-x), 0 < x < 1 Find the variance and standard deviation of X

Let 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.…