The joint probability density function for X and Y is f(x, y). Find P(X < 0.3| Y = 0.4). Remember, you need to find the conditional density for X at Y = 0.4, then do the appropriate integration. + (2х + у) 0
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- While taking a walk along the road where you live, you accidentally drop your glove, but you don't know where. The probability density p(x) for having dropped the glove a kilometers from home (along the road) is -4x p(x) = 4e for x > 0 a. What is the probability that you dropped it within 1 kilometer of home? b. At what distance y from home is the probability that you dropped it within y km of home equal to 0.95? kmThe random variable X models the loss in thousands of dollars due to a fire in a commercial building. Its density function is f(x) = 0.005*(20-x) for 0 being less than or equal to x and x being less than or equal to 20 and f(x)= 0 otherwise. Given that a loss due to the fire exceeds $8000, find the probability the loss exceeds $16000.Find the probability density function of Y = X2. Make sure that you show all the steps.
- Suppose that X is a normal random variable with parameters u = 5 and o = 1. Define Y = X2 – 10X + 25. Then what is the probability density function of Y (fy(y)). Probability TheoryWhile taking a walk along the road where you live, you accidentally drop your glove, but you don't know where. The probability density p(x) for having dropped the glove a kilometers from home (along the road) is p(x) = 2e-2 for x ≥ 0 a. What is the probability that you dropped it within 1 kilometer of home? I b. At what distance y from home is the probability that you dropped it within y km of home equal to 0.95? km <-|Y has a density function + y, Osys1, Ry) = {7 0, elsewhere. Find the mean and variance of Y. (Round your answers to four decimal places.) E(Y) = V(Y) =
- The density function of the random variable X is given by Px (x) = V2 T o The random variables X and Y are related as Y= X. Find the density function of variable Y.While taking a walk along the road where you live, you accidentally drop your glove, but you don't know where. The probability density p(x) for having dropped the glove x kilometers from home (along the road) is -5x p(x) = 5e for x ≥ 0 a. What is the probability that you dropped it within 1 kilometer of home? J b. At what distance y from home is the probability that you dropped it within y km of home equal to 0.95? km ←The probability density function of a distribution is given by x f(x) = exp(-7). Use differentiation to show that the probability density function has a maximum at x = 0. The moment generating function of a distribution is M(t) = (q + pet)", where p € [0, 1], q = 1 - p and n is a positive integer. Use the moment generating function to find the mean and variance of the distribution in terms of p, q and n.
- While taking a walk along the road where you live, you accidentally drop your glove, but where. The probability density p(x) for having dropped the glove a kilometers from home (along the road) is you don't know -8x p(x) = 8e for x > 0 a. What is the probability that you dropped it within 1 kilometer of home? b. At what distance y from home is the probability that you dropped it within y km of home equal to 0.95? kmDetermine the conditional probability distribution of Y given that X = 2. Where the joint probability density function is given by f(x,y)= 1 - (x + y) for 1 < x < 4 and 0 < y < 3.Two components of a laptop computer have the following joint probability density function for their useful lifetimes X and Y (in years): f(x, y)= xe (1+ y) x20, y20 otherwise Find the marginal probability density function of X, fy(x).