The error in the length of a part, in mm, is a random variable X with probability density function f(x)=12(x² -x'), 0sxsl a. Find the mean error. b. Find the variance of the error. The error must be less than 0.8 mm for the part to be fit properly. What proportion of the parts will fit properly? с.

let X and Y are two random variables with p.d.f as f(x,y)=3x2y+3yx2 0<x<1 0<x<1.find conditional density of X given Y?.Find mean mode and standard deviation of r.v Y?. Correlation between X and Y?. check that X and Y are independent or not?.

сх 4. Elongation (in percent) of treated metal plates are random with probability density function: f (x) = ,5 < x < 25 600 Find the value of c which makes f(x) a properly defined pdf. Find the variance of elongation. а. b. Find the probability that the elongation is between 10% and 15% or between 12% and 20%. That is if E is the random variable representing elongation, find P(10 < E < 15 or 12 < E < 20). с.

1 Given the probability density function f(x) = 4 over the interval [1, 5], find the expected value, the mean, the variance and the standard deviation. Expected value: Мean: Variance: Standard Deviation:

Suppose that X, Y are independent standard normal RVs. Find the joint pdf of Z, W where Z = XY, W = 3X – 2Y.

An insurer's annual weather related loss, X, is a random variable with density function   f(x) = 2.5 (200)2.5 / x3.5 for x >= 200 and 0 otherwise.   Calculate the 30th percentiles of X. (Round to 2 decimals).

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Data are obtained on the location of incidents on a 12-kilometer-long bridge. The distribution of the distance along the bridge (in kilometers) where an incident occurs is depicted in the density curve below. 12 Distance (kilometers) along the bridge where an accident occurs 12 1. The probability of an incident that occurs in any 4 kilometers long bridge segment is always distributed over any 4-kilometer interval. A. 1/3, uniformly B. 1/3, not uniformly C. 1/6, uniformly D. 1/2, not uniformly To put it another way, the probability is 2. What is P(9 < X < 12)? 1 Same as P(2 < X < 5). 2. Same as P(2 s X < 5). 3. Same as P(2 < X < 5). 4. Same as P(2 < X < 5). A. 1 B. 1 and 2 C. 2, 3, and 4 D. 1. 2. 3, and 4