The joint probability density of X and Y is f(x, y). Find the marginal density of X at 0.4. The answer should be given to 2 decimal places. g(0.4) = f(x, y)= { 2(x + y) 0

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 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 <-|

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.

Let X and Y have the joint pdf f(x,y)= x+y , 0<=x<=1, 0<=y<=1.    Find the marginal fx(x) and fy(y). Show if f(x,y) dependent.  Compute mean(x), mean(y), variance (x) and variance(y)

The lifetime of a machine part has a continuous distribution on the interval (0,45) months with probability density function f, where f(x) is proportional to (4+x)-2. Find the probability that the lifetime of the machine part is less than 7 months.

The density function for a random variable X is f(x). The answer should be given to 4 decimal places. (2e-2x X > 0 f (x) = { elsewhere P(X = 2.5) =

Suppose that X and Y have a joint probability density function given by ce-3z=5y if a, y 20 fx.y(T, y) = otherwise Find the marginal probability density function fx and state the name of the distribution of X.

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).