Let X1 have the density function .3 4x;, f,(x,) = 0, 0

11. Let X be a continuous random variable with probability density function r>0 f(x)= 0, otherwise, where 1> 0. Let Y be the largest integer less than or equal to X. Determine the probability function of Y.

Hi. Please help. I need to calculate the mean and vairance of the probabiltiy density function I am getting one minute but the time better each serving is at least 2 minutes. Can you correct me as I have gone wrong somewhere. (see attached doc)

A number x is selected at random from [4, 20]. The probability density function for x is given by f(x) = for 4 ≤ x ≤ 20. 2 Find the probability that a number selected is in the sub-interval [7, 18].

Please answer number 4

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.…